Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant chal...Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.展开更多
Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totall...Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.展开更多
This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation ...This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation accuracy and robustness.We employ a manifold-based optimization approach,leveraging exponential and logarithmic mappings to transform rotation vectors into rotation matrices.The proposed ESKF framework ensures state variables remain near the origin,effectively mitigating singularity issues and enhancing numerical stability.Additionally,due to the small magnitude of state variables,second-order terms can be neglected,simplifying Jacobian matrix computation and improving computational efficiency.Furthermore,we introduce a novel Kalman filter gain computation strategy that dynamically adapts to low-dimensional and high-dimensional observation equations,enabling efficient processing across different sensor modalities.Specifically,for resource-constrained UAV platforms,this method significantly reduces computational cost,making it highly suitable for real-time UAV applications.展开更多
Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two...Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two new microchannel structures:V-type and A-type.The effects of various structural parameters of the manifolds on the velocity distribution are reported.The V-type and A-type microchannel plates had a more uniform velocity distribution compared to the Z-type microchannel plate.The final result showed that it is beneficial for the V-type microchannel plate to obtain a more uniform velocity distribution when the manifold structure parameters are X_(in)=-1,X_(out)=0,Y_(in)=10,Y_(out)=6,Hin=4,H_(out)=1,and R=0.5.展开更多
This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault dia...This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault diagnosis of a reciprocating compressor(RC).Initially,raw vibration signals undergo empirical mode decomposition to break them down into multiple intrinsic mode functions(IMFs).This operation can reveal inherent vibration patterns of fault and other components hidden in the original signals.Subsequently,features are refined from all the IMFs and concatenated into a high-dimensional representative vector,offering localized and comprehensive insights into RC operation.Through DBN,the fault-sensitive information is further refined from the features to enhance their performance in fault identification.Finally,similarities among subspaces on the Grassmann manifold are computed to match fault types.The efficacy of the method is validated usingfield data.Comparative analysis with traditional approaches for feature dimension reduction,feature extraction,and Euclidean distance-based fault identification underscores the effectiveness and superiority of the proposed method in RC fault diagnosis.展开更多
There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are di...There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are difficult to discover unknown signals while recognizing known ones.In this paper,a compact manifold mixup feature-based open-set recognition approach(OR-CMMF)is proposed to address the above problem.First,the proposed approach utilizes the center loss to constrain decision boundaries so that it obtains the compact latent signal feature representations and extends the low-confidence feature space.Second,the latent signal feature representations are used to construct synthetic representations as substitutes for unknown categories of signals.Then,these constructed representations can occupy the extended low-confidence space.Finally,the proposed approach applies the distillation loss to adjust the decision boundaries between the known categories signals and the constructed unknown categories substitutes so that it accurately discovers unknown signals.The OR-CMMF approach outperformed other state-of-the-art open-set recognition methods in comprehensive recognition performance and running time,as demonstrated by simulation experiments on two public datasets RML2016.10a and ORACLE.展开更多
In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is ...In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.展开更多
In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curv...In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.展开更多
In this paper,we introduce the notion of f-CC harmonic maps with potential H from a Riemannian manifold into sub-Riemannian manifolds,and achieve some vanishing theorems for f-CC harmonic maps with potential H via the...In this paper,we introduce the notion of f-CC harmonic maps with potential H from a Riemannian manifold into sub-Riemannian manifolds,and achieve some vanishing theorems for f-CC harmonic maps with potential H via the stress-energy tensor and the monotonicity formulas.展开更多
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock mater...The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.展开更多
Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
Proves that cosymplectic hypersurfaces of six dimensional Hermitian submanifolds of the octave algebra are ruled manifolds and establishes a necessary and sufficient condition for a cosymplectic hypersurface of Hermit...Proves that cosymplectic hypersurfaces of six dimensional Hermitian submanifolds of the octave algebra are ruled manifolds and establishes a necessary and sufficient condition for a cosymplectic hypersurface of Hermitian M 6 O to be a minimal submanifold of M 6.展开更多
The necessary and sufficient conditions for an arbitrary almost Hermitian manifold to be an R 2 or a cR 2 manifold are established. Some examples of non Khlerian and non nearly Khlerian R 2 and cR 2 manifolds are ...The necessary and sufficient conditions for an arbitrary almost Hermitian manifold to be an R 2 or a cR 2 manifold are established. Some examples of non Khlerian and non nearly Khlerian R 2 and cR 2 manifolds are given.展开更多
In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we e...In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we explore some works in the special area in Di erential Geometry,Lie Group and Complex Homogeneous Space.Together with the special area in nonlinear analysis on complex manifolds,they are the two major aspects of my research interests.展开更多
In this work,it is proved that every isotropic Weyl manifold with a semi- symmetric connection is locally conformal to an Einstein manifold with a semi-symmetric connection.
Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard to...Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.展开更多
Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star （cf. [9]）. The studies on warped product ma...Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star （cf. [9]）. The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen＇s work on CR-warped product submanifolds of Kaehler manifolds （cf. [6], [7]）. Later on, similar studies were carried out in the setting of 1.c.K. manifolds and nearly Kaehler manifolds （el. [3], [11]）. In the present article, we investigate a larger class of warped product submanifolds of 1.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold.展开更多
We give a necessary and sufficient condition for an almost Hermitian manifold to be a Kahler manifold. By making use of this condition, we give a new proof of Goldberg＇s theorem.
A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of...A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.展开更多
文摘Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.
文摘Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.
基金National Natural Science Foundation of China(Grant No.62266045)National Science and Technology Major Project of China(No.2022YFE0138600)。
文摘This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation accuracy and robustness.We employ a manifold-based optimization approach,leveraging exponential and logarithmic mappings to transform rotation vectors into rotation matrices.The proposed ESKF framework ensures state variables remain near the origin,effectively mitigating singularity issues and enhancing numerical stability.Additionally,due to the small magnitude of state variables,second-order terms can be neglected,simplifying Jacobian matrix computation and improving computational efficiency.Furthermore,we introduce a novel Kalman filter gain computation strategy that dynamically adapts to low-dimensional and high-dimensional observation equations,enabling efficient processing across different sensor modalities.Specifically,for resource-constrained UAV platforms,this method significantly reduces computational cost,making it highly suitable for real-time UAV applications.
基金supported by Scientific Research Project of Guangdong Provincial Department of Education(2024KQNCX152).
文摘Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two new microchannel structures:V-type and A-type.The effects of various structural parameters of the manifolds on the velocity distribution are reported.The V-type and A-type microchannel plates had a more uniform velocity distribution compared to the Z-type microchannel plate.The final result showed that it is beneficial for the V-type microchannel plate to obtain a more uniform velocity distribution when the manifold structure parameters are X_(in)=-1,X_(out)=0,Y_(in)=10,Y_(out)=6,Hin=4,H_(out)=1,and R=0.5.
文摘This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault diagnosis of a reciprocating compressor(RC).Initially,raw vibration signals undergo empirical mode decomposition to break them down into multiple intrinsic mode functions(IMFs).This operation can reveal inherent vibration patterns of fault and other components hidden in the original signals.Subsequently,features are refined from all the IMFs and concatenated into a high-dimensional representative vector,offering localized and comprehensive insights into RC operation.Through DBN,the fault-sensitive information is further refined from the features to enhance their performance in fault identification.Finally,similarities among subspaces on the Grassmann manifold are computed to match fault types.The efficacy of the method is validated usingfield data.Comparative analysis with traditional approaches for feature dimension reduction,feature extraction,and Euclidean distance-based fault identification underscores the effectiveness and superiority of the proposed method in RC fault diagnosis.
基金fully supported by National Natural Science Foundation of China(61871422)Natural Science Foundation of Sichuan Province(2023NSFSC1422)Central Universities of South west Minzu University(ZYN2022032)。
文摘There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are difficult to discover unknown signals while recognizing known ones.In this paper,a compact manifold mixup feature-based open-set recognition approach(OR-CMMF)is proposed to address the above problem.First,the proposed approach utilizes the center loss to constrain decision boundaries so that it obtains the compact latent signal feature representations and extends the low-confidence feature space.Second,the latent signal feature representations are used to construct synthetic representations as substitutes for unknown categories of signals.Then,these constructed representations can occupy the extended low-confidence space.Finally,the proposed approach applies the distillation loss to adjust the decision boundaries between the known categories signals and the constructed unknown categories substitutes so that it accurately discovers unknown signals.The OR-CMMF approach outperformed other state-of-the-art open-set recognition methods in comprehensive recognition performance and running time,as demonstrated by simulation experiments on two public datasets RML2016.10a and ORACLE.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.12201314).
文摘In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.
基金supported by Guangzhou Science and Technology Program(202102021174)Guangdong Basic and Applied Basic Research Foundation(2023A1515012121).The second author was supported by the Natural Science Foundation of Jiangsu Province(BK20230900)+1 种基金the Fundamental Research Funds for the Central Universities(30924010838)Both authors are partially supported by NSF in China(12141104).
文摘In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.
基金Supported by the National Natural Science Foundation of China(12271254,12141104,12571056)supported by Natural Science Foundation of Henan(252300421791,252300421497)。
文摘In this paper,we introduce the notion of f-CC harmonic maps with potential H from a Riemannian manifold into sub-Riemannian manifolds,and achieve some vanishing theorems for f-CC harmonic maps with potential H via the stress-energy tensor and the monotonicity formulas.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
基金supported by the National Natural Science Foundation of China(Grant Nos.42172312 and 52211540395)support from the Institut Universitaire de France(IUF).
文摘The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
文摘Proves that cosymplectic hypersurfaces of six dimensional Hermitian submanifolds of the octave algebra are ruled manifolds and establishes a necessary and sufficient condition for a cosymplectic hypersurface of Hermitian M 6 O to be a minimal submanifold of M 6.
文摘The necessary and sufficient conditions for an arbitrary almost Hermitian manifold to be an R 2 or a cR 2 manifold are established. Some examples of non Khlerian and non nearly Khlerian R 2 and cR 2 manifolds are given.
基金the Natural Science Foundation of Henan University。
文摘In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we explore some works in the special area in Di erential Geometry,Lie Group and Complex Homogeneous Space.Together with the special area in nonlinear analysis on complex manifolds,they are the two major aspects of my research interests.
文摘In this work,it is proved that every isotropic Weyl manifold with a semi- symmetric connection is locally conformal to an Einstein manifold with a semi-symmetric connection.
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.
基金supported by the research grant(162/428)of the Research centre,faculty of Science,King Abdul Aziz University, K.S.A
文摘Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star （cf. [9]）. The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen＇s work on CR-warped product submanifolds of Kaehler manifolds （cf. [6], [7]）. Later on, similar studies were carried out in the setting of 1.c.K. manifolds and nearly Kaehler manifolds （el. [3], [11]）. In the present article, we investigate a larger class of warped product submanifolds of 1.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold.
文摘We give a necessary and sufficient condition for an almost Hermitian manifold to be a Kahler manifold. By making use of this condition, we give a new proof of Goldberg＇s theorem.
文摘A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.
