By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)of Fischer...By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)of Fischer–Marsden equation on real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadric Q^(m∗).Next,as an application we also show that there does not exist a non-trivial solution(g,ν)of the Fischer–Marsden equation on contact real hypersurfaces in the complex hyperbolic quadric Q^(m∗).Consequently,the Fischer–Marsden conjecture is true on these two kinds of real hypersurfaces in the complex hyperbolic quadric Q^(m∗).展开更多
This paper points out that equations （18a） and （18b） in Ref. [7] [Gao Y J 2008 Chin. Phys. B 17 3574] only possess the solutions M = ργc. So, there does not exist the so-called soliton solution family for the Ei...This paper points out that equations （18a） and （18b） in Ref. [7] [Gao Y J 2008 Chin. Phys. B 17 3574] only possess the solutions M = ργc. So, there does not exist the so-called soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields shown in Ref. [7].展开更多
The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural...The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural Riemann- Hilbert （RH） transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU（p ＋ 1, 1） and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author＇s paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.展开更多
We get an explicit lower bound for the radius of a Bergman ball contained in the Dirichlet fundamental polyhedron of a torsion free discrete group G PU（n,1）acting on complex hyperbolic space.As an application,we als...We get an explicit lower bound for the radius of a Bergman ball contained in the Dirichlet fundamental polyhedron of a torsion free discrete group G PU（n,1）acting on complex hyperbolic space.As an application,we also give a lower bound for the volumes of complex hyperbolic n-manifolds.展开更多
We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negative...We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.展开更多
Given an arithmetic lattice of the unitary group U(3,1)arising from a hermitian form over a CM-field,we show that all unitary representations of U(3,1)with nonzero cohomology contribute to the cohomology of the attach...Given an arithmetic lattice of the unitary group U(3,1)arising from a hermitian form over a CM-field,we show that all unitary representations of U(3,1)with nonzero cohomology contribute to the cohomology of the attached arithmetic complex 3-manifold,at least when we pass to a finite-index subgroup of the given arithmetic lattice.展开更多
The paper has two parts.We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations.We will mainly focus on some of the ...The paper has two parts.We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations.We will mainly focus on some of the recent studies of Bishop surfaces,which,in particular,includes the work of the authors.In the second part of the paper,we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant.More precisely,we let M be a real submanifold of C 2 defined by an equation of the form w=zz+2Re(z s+az s+1)with s≥3 and a a complex parameter.We will prove in the second part of the paper that for s≥4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation.When s=3,we show that surfaces of this type with two different real parameters are not holomorphically equivalent.展开更多
The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the sta...The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the stability of such gridconnected inverter systems currently involves using a complex hyperbolic function to shaped model of the transmission line circuit.This has proved to be problematic,so,drawing upon the distribution parameter characteristics of transmission lines,this paper looks at how to use impedance-based stability criteria to assess the stability of multi-paralleled grid-connected inverters.First,the topology of multi-paralleled inverters connected to the grid via transmission lines is established,using each transmission line terminal as a grid connection point.Each grid-connected system is taken to be equivalent to a small-signal circuit model of the“current source-grid”.Euler’s formula and the Nyquist stability criterion are combined to assess the stability of the associated grid-connected current transfer functions and evaluate the stability of the grid-connected current.Finally,a simulation analysis circuit is constructed to verify whether power line intervention will cause stability problems in the grid-connected system.Overall,it is found that long-distance transmission lines are more likely to cause unstable output of the grid-connected current.It is also found that the number of grid-connected inverters,the short-circuit ratio(SCR),the distorted grid and the inverter parameters can all have a significant impact on the stability of the grid-connected current.展开更多
We generalize Bangert＇s non-hyperbolicity result for uniformly tamed almost complex structures on standard symplectic R^2n to asymptotically standard symplectic manifolds.
基金supported by Grants Proj.No.NRF-2018-R1D1A1B-05040381&NRF-2021-R1C1C-2009847 from National Research Foundation of Korea.
文摘By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)of Fischer–Marsden equation on real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadric Q^(m∗).Next,as an application we also show that there does not exist a non-trivial solution(g,ν)of the Fischer–Marsden equation on contact real hypersurfaces in the complex hyperbolic quadric Q^(m∗).Consequently,the Fischer–Marsden conjecture is true on these two kinds of real hypersurfaces in the complex hyperbolic quadric Q^(m∗).
文摘This paper points out that equations （18a） and （18b） in Ref. [7] [Gao Y J 2008 Chin. Phys. B 17 3574] only possess the solutions M = ργc. So, there does not exist the so-called soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields shown in Ref. [7].
基金Project supported by the Science Foundation from Education Department of Liaoning Province, China （Grant No 202142036） and the National Natural Science Foundation of China （Grant No 10475036）.
文摘The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural Riemann- Hilbert （RH） transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU（p ＋ 1, 1） and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author＇s paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
基金supported by National Natural Science Foundation of China(Grant Nos.10671059 and 11201134)Young Teachers Support Program of Hunan University(Grant No.531107040021)
文摘We get an explicit lower bound for the radius of a Bergman ball contained in the Dirichlet fundamental polyhedron of a torsion free discrete group G PU（n,1）acting on complex hyperbolic space.As an application,we also give a lower bound for the volumes of complex hyperbolic n-manifolds.
文摘We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.
基金J.-S.Li was supported in part by RGC-GRF grant 602410 of HKSAR.B.Sun was supported in part by NSFC Grant 11222101.
文摘Given an arithmetic lattice of the unitary group U(3,1)arising from a hermitian form over a CM-field,we show that all unitary representations of U(3,1)with nonzero cohomology contribute to the cohomology of the attached arithmetic complex 3-manifold,at least when we pass to a finite-index subgroup of the given arithmetic lattice.
基金supported in part by US National Science Foundation(Grant No.0801056)supported in part by National Natural Science Foundation of China(Grant No.10901123)+1 种基金Research Fund for the Doctoral Program of Higher Education of China(Grant No.20090141120010)Ky and Yu-Fen Fan Fund from American Mathematical Society,and a research fund from Wuhan University(Grant No.1082002)
文摘The paper has two parts.We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations.We will mainly focus on some of the recent studies of Bishop surfaces,which,in particular,includes the work of the authors.In the second part of the paper,we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant.More precisely,we let M be a real submanifold of C 2 defined by an equation of the form w=zz+2Re(z s+az s+1)with s≥3 and a a complex parameter.We will prove in the second part of the paper that for s≥4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation.When s=3,we show that surfaces of this type with two different real parameters are not holomorphically equivalent.
文摘The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the stability of such gridconnected inverter systems currently involves using a complex hyperbolic function to shaped model of the transmission line circuit.This has proved to be problematic,so,drawing upon the distribution parameter characteristics of transmission lines,this paper looks at how to use impedance-based stability criteria to assess the stability of multi-paralleled grid-connected inverters.First,the topology of multi-paralleled inverters connected to the grid via transmission lines is established,using each transmission line terminal as a grid connection point.Each grid-connected system is taken to be equivalent to a small-signal circuit model of the“current source-grid”.Euler’s formula and the Nyquist stability criterion are combined to assess the stability of the associated grid-connected current transfer functions and evaluate the stability of the grid-connected current.Finally,a simulation analysis circuit is constructed to verify whether power line intervention will cause stability problems in the grid-connected system.Overall,it is found that long-distance transmission lines are more likely to cause unstable output of the grid-connected current.It is also found that the number of grid-connected inverters,the short-circuit ratio(SCR),the distorted grid and the inverter parameters can all have a significant impact on the stability of the grid-connected current.
文摘We generalize Bangert＇s non-hyperbolicity result for uniformly tamed almost complex structures on standard symplectic R^2n to asymptotically standard symplectic manifolds.
