Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal...Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold. Further, an almost hyper Hermitian structure has been constructed on the tangent bundle TM with help of the Riemannian connection of an almost Hermitian structure on a manifold M then, we consider an embedding of the almost Hermitian manifold M in the corresponding normal tubular neighborhood of the null section in the tangent bundle TM equipped with the deformed almost hyper Hermitian structure of the special form. As a result, we have obtained that any Riemannian manifold M of dimension n can be embedded as a totally geodesic submanifold in a Kaehlerian manifold of dimension 2n (Theorem 6) and in a hyper Kaehlerian manifold of dimension 4n (Theorem 7). Such embeddings are “good” from the point of view of Riemannian geometry. They allow solving problems of Riemannian geometry by methods of Kaehlerian geometry (see Section 5 as an example). We can find similar situation in mathematical analysis (real and complex).展开更多
Six-dimensional Hermitian submanifolds of Cayley algebra are considered.It is proved that if such a submanifold of the octave algebta complies with the U-Kenmotsu hypersurfaces axiom,then it is Khlerian.
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 main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres.As a consequence,complex structures on S^(1)×S^(7)×S^(6),and on S^(10...The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres.As a consequence,complex structures on S^(1)×S^(7)×S^(6),and on S^(10)×S^(3)×S(2)with vanishing first Chern class,are built.展开更多
In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.
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
The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasa...The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasaki) is a Sasakian manifold homothetic with a generalized Berger sphere, and that a natural Cartan structure is arising from the horizontal 1-forms and the author associates a non-Einstein pseudo-Hermitian structure. Also, one studies when the Sasaki type metric of T_1S is generally adapted to the natural co-frame provided by the Finsler structure.展开更多
In this article,we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in C n+1.Then we survey some results on the spectral zeta function which is induced by the trace of the he...In this article,we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in C n+1.Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel.In the second part of the paper,we discuss an isospectral problem in the CR setting.展开更多
In this paper,we study the displacement rank of the Core-EP inverse.Both Sylvester displacement and generalized displacement are discussed.We present upper bounds for the ranks of the displacements of the Core-EP inve...In this paper,we study the displacement rank of the Core-EP inverse.Both Sylvester displacement and generalized displacement are discussed.We present upper bounds for the ranks of the displacements of the Core-EP inverse.Numerical experiments are presented to demonstrate the efficiency and accuracy.展开更多
文摘Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold. Further, an almost hyper Hermitian structure has been constructed on the tangent bundle TM with help of the Riemannian connection of an almost Hermitian structure on a manifold M then, we consider an embedding of the almost Hermitian manifold M in the corresponding normal tubular neighborhood of the null section in the tangent bundle TM equipped with the deformed almost hyper Hermitian structure of the special form. As a result, we have obtained that any Riemannian manifold M of dimension n can be embedded as a totally geodesic submanifold in a Kaehlerian manifold of dimension 2n (Theorem 6) and in a hyper Kaehlerian manifold of dimension 4n (Theorem 7). Such embeddings are “good” from the point of view of Riemannian geometry. They allow solving problems of Riemannian geometry by methods of Kaehlerian geometry (see Section 5 as an example). We can find similar situation in mathematical analysis (real and complex).
文摘Six-dimensional Hermitian submanifolds of Cayley algebra are considered.It is proved that if such a submanifold of the octave algebta complies with the U-Kenmotsu hypersurfaces axiom,then it is Khlerian.
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.
基金The project is partially supported by the NSFC(11871282,11931007)BNSF(Z190003)Nankai Zhide Foundation.
文摘The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres.As a consequence,complex structures on S^(1)×S^(7)×S^(6),and on S^(10)×S^(3)×S(2)with vanishing first Chern class,are built.
文摘In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.
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The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasaki) is a Sasakian manifold homothetic with a generalized Berger sphere, and that a natural Cartan structure is arising from the horizontal 1-forms and the author associates a non-Einstein pseudo-Hermitian structure. Also, one studies when the Sasaki type metric of T_1S is generally adapted to the natural co-frame provided by the Finsler structure.
基金supported by National Security Agency,United States Army Research Offfice and a Hong Kong RGC Competitive Earmarked Research (Grant No. 600607)
文摘In this article,we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in C n+1.Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel.In the second part of the paper,we discuss an isospectral problem in the CR setting.
基金Supported by Guangxi Natural Science Foundation(2018GXNSFDA281023,2018GXNSFAA138181)High Level Innovation Teams and Distinguished Scholars in Guangxi Universities(GUIJIAOREN201642HAO)+3 种基金Graduate Research Innovation Project of Guangxi University for Nationalities(gxun-chxzs2018041,gxun-chxzs2019026)the Special Fund for Bagui Scholars of Guangxi(2016A17)the National Natural Science Foundation of China(61772006,12061015)the Science and Technology Major Project of Guangxi(AA17204096)。
文摘In this paper,we study the displacement rank of the Core-EP inverse.Both Sylvester displacement and generalized displacement are discussed.We present upper bounds for the ranks of the displacements of the Core-EP inverse.Numerical experiments are presented to demonstrate the efficiency and accuracy.
