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
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
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
In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe ...In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.展开更多
The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant sol...The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant solution of -1/f2 Jφ（dφ（grad（lnb）））＋n/2 grad｜dφ（grad（lnb））｜2=0 and f is a non-constant solution of -1/b2Jψ（dψ（grad（lnf）））＋m/2grad｜dψ（grad（lnf））｜2=0, and Φ2=φ×ψ is a proper biharmonic map if and only if φ-and ψ-are proper biharmonic maps.展开更多
We study a Riemannian manifolds M with a f-structures. If the tangent bundle of the Riemannian manifolds is TM=DD⊥ dimD=2P,dimD⊥=q=n-2p≥1. We can define a generalized contact manifolds, get some property of it.
We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radic...We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.展开更多
In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, m...In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.展开更多
In this study,we concluded the Hamiltonian equations on(M3,φ,ξ,η,g𝑔),being a model.Finally introduce,some geometrical and physical results on the related mechanic systems have been discussed.
In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped ...In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.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
In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we...In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive(resp.non-negative)ℓ-second Ricci curvature to a Hermitian manifold with non-positive(resp.negative)real bisectional curvature.These theorems generalize the results[5,6]proved recently by L.Ni on Kähler manifolds to Hermitian manifolds.We also derive an integral inequality for a holomorphic map between Hermitian manifolds.展开更多
This paper presents the design of sliding mode controller for the output regulation of single input single output （SISO） nonlinear systems. The sliding surfaces are designed to force the error dynamics to follow pro...This paper presents the design of sliding mode controller for the output regulation of single input single output （SISO） nonlinear systems. The sliding surfaces are designed to force the error dynamics to follow proportional （P）, proportional integral （PI） and proportional integral derivative （PID） dynamics. The controller parameters are obtained using probabilistic particle swarm optimization technique. A judicious selection of various sliding surfaces based on the relative degree of the systems is also elaborated. A detailed comparison of the output regulation for various systems with different relative degree is presented. Numerical simulation shows the effectiveness of the proposed method and robustness of the sliding mode controller.展开更多
The Koppelman-Leray formula on complex manifolds is obtained, and under suitable condition the continuous solution of partial derivative-equation on complex manifolds is obtained.
This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.
In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Ki...In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.展开更多
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.
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 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 National Natural Science Foundation of China under Grant No.10801027Fok Ying Tong Education Foundation under Grant No.121003
文摘In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.
基金The National Natural Science Foundation of China(No.10971029)
文摘The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant solution of -1/f2 Jφ（dφ（grad（lnb）））＋n/2 grad｜dφ（grad（lnb））｜2=0 and f is a non-constant solution of -1/b2Jψ（dψ（grad（lnf）））＋m/2grad｜dψ（grad（lnf））｜2=0, and Φ2=φ×ψ is a proper biharmonic map if and only if φ-and ψ-are proper biharmonic maps.
文摘We study a Riemannian manifolds M with a f-structures. If the tangent bundle of the Riemannian manifolds is TM=DD⊥ dimD=2P,dimD⊥=q=n-2p≥1. We can define a generalized contact manifolds, get some property of it.
文摘We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.
文摘In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.
文摘In this study,we concluded the Hamiltonian equations on(M3,φ,ξ,η,g𝑔),being a model.Finally introduce,some geometrical and physical results on the related mechanic systems have been discussed.
文摘In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.
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.
基金supported by National Natural Science Foundation of China(12001490)Natural Science Foundation of Zhejiang Province(LQ20A010005).
文摘In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive(resp.non-negative)ℓ-second Ricci curvature to a Hermitian manifold with non-positive(resp.negative)real bisectional curvature.These theorems generalize the results[5,6]proved recently by L.Ni on Kähler manifolds to Hermitian manifolds.We also derive an integral inequality for a holomorphic map between Hermitian manifolds.
文摘This paper presents the design of sliding mode controller for the output regulation of single input single output （SISO） nonlinear systems. The sliding surfaces are designed to force the error dynamics to follow proportional （P）, proportional integral （PI） and proportional integral derivative （PID） dynamics. The controller parameters are obtained using probabilistic particle swarm optimization technique. A judicious selection of various sliding surfaces based on the relative degree of the systems is also elaborated. A detailed comparison of the output regulation for various systems with different relative degree is presented. Numerical simulation shows the effectiveness of the proposed method and robustness of the sliding mode controller.
文摘The Koppelman-Leray formula on complex manifolds is obtained, and under suitable condition the continuous solution of partial derivative-equation on complex manifolds is obtained.
基金Supported by the NNSF of China(10231010)the Trans-Century Training Programme Foundation for Talents by the Ministry of Education of China+1 种基金the Natural Science Foundation of Zhejiang Province(101037) Fudan Postgraduate Students Innovation Project(CQH5928002)
文摘This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.
文摘In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.
