子流形与拓扑球面定理

本文建立了球面Sn p(c) (c>0 )中的完备子流形的一个拓扑球面定理 ,结果表明完备子流形的拓扑是受其内在和外在曲率不变量满足的某些条件所影响的     

欧氏空间中子流形的曲率与几何性质

研究了欧氏空间En p中具常数量曲率n(n-1)r的n(n>2)维完备连通子流形,得到了En p截面曲率非负且法联络平坦的完备连通子流形的一个分类定理.     

复射影空间中具有常数量曲率的完备全实子流形

本文研究了复射影空间中具有常数量曲率的完备全实子流形的问题.利用丘成桐的广义极大值原理和自伴随算子,获得了这类子流形的某些内蕴刚性定理.     

关于局部对称空间中的伪脐子流形

本文讨论了局部对称完备黎曼流形中的紧致伪脐子流形,且具有平行平均山率向量场。得到了这类子流形成为全脐子流形及其余维数减小的几个拼挤定理。     

关于局部对称空间中极小子流形的一个Ricci曲率pinching定理

研究局部对称空间中具有正Ricci曲率的完备极小子流形,得到了关于子流形Ricci曲率的一个pinching定理,把Norio Ejiri的结论从外围空间为球空间推广到局部对称空间中。     

欧氏空间中完备极小子流形

在一个类似于稳定不等式的条件下,得到了欧氏空间中完备极小子流形的Bernstein型定理.我们的结果部分推广了Li H.Z.和Wei G.X.的定理.     

不定复空间型中具有平行平均曲率向量的完备全实类空子流形

利用活动标架法和广义极大值原理研究了不定复射影空间中完备的具有平行平均曲率向量的全实类空子流形,得到这类子流形的Pinching定理.     

关于局部对称空间中的极小子流形

本文研究局部对称完备黎曼流形中的紧致极小流形，得到了这类子流形的第二基本形式模长平方的一个拼挤定理，推广了［１］中的结论．     

关于局部对称空间中2-调和子流形

本文研究局部对称完备黎曼流形中的紧致2－调和子流形，得到了这类流形第二基本模式长平方的Pinching定理及推广的J．Simons型积分不等式。     

非正曲率流形及其子流形上有界区域的特征值

本文研究了完备单连通具有非正曲率黎曼流形及其子流形上有界区域的特征值问题.利用广义Hessian比较定理,获得了局部特征值的下界估计式,将McKean[2]的定理在局部上推广到了非正曲率的情形.     

复射影空间CP~((n+p)/2)中具有2-调和的一般子流形

本文研究了复射影空间中具有2-调和的一般子流形问题.利用活动标架法,获得了这类子流形成为极小子流形的Pinching定理和Simons型积分不等式,此外还得到关于2-调和伪脐一般子流形的一个刚性定理,推广了复射影空间中具有2-调和全实子流形的一些相应结果.     

Transversality on infinite dimensional manifolds with corners

In this paper we study transversality on infinite dimensional manifolds with corners. We deal with transversality, boundary-transversality and weak-boundary-transversality, characterize these three notions by means of the infinitesimal transversality, construct submanifolds as inverse image of submanifolds by transversal maps and prove parametrized theorems about the density of weak-boundary-transversality and boundary-transversality, which generalize the corresponding Abraham and Quinn theorems.     

Finite Type Non—Minimal Submanifolds

The notion of finite type xubmanifolds was introduced by B.Y.Chen.In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds.The characteristic theorems of 2-type Chen submanifolds、mass-symmetric hypersurfaces and Dupin hypersurfaces in Es^m are obtained.The classification theorems of 3-type hypersurfaces and null 2-type curves in Es^m are also proved.     

Generalized Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds

We study a class of submanifolds, called Generalized Cauchy-Riemann (GCR) lightlike submanifolds of indefinite Sasakian manifolds as an umbrella of invariant, screen real, contact CR lightlike subcases [8] and real hypersurfaces [9]. We prove existence and non-existence theorems and a characterization theorem on minimal GCR-lightlike submanifolds.     

On Affine Geometry of Purley Real Submanifolds

We propose to study n-dimensional purely real submanifolds of the standard affine complex space Cⁿ from an affine point of view. Such submanifolds are naturally endowed with a unique transversal bundle. Fundamental theorems are given as well as a theorem of Cartan–Norden type. Examples illustrating particular affine properties of such submanifolds are provided.     

Indefinite Kähler submanifolds with positive index of relative nullity

We deal with complex submanifolds in indefinite space forms. In particular, submanifolds with large index of relative nullity are emphasized. In that context, we prove cylinder theorems in terms of indefinite metrics. We also give a systematic way of constructing a family of new complete and closed indefinite complex submanifolds in the projective setting.In the appendix, we show that the method used for complex cases can be applied to real indefinite geometry. We prove real cylinder theorems including B-scrolls in the general signature. We also show two decomposition lemmas which clarify the relationships between the Hartman-Nirenberg cylinder theorem and slanted cylinder theorems in indefinite geometry.     

Some Bernstein-type rigidity theorems

We prove some Bernstein-type rigidity theorems for complete submanifolds in a Euclidean space and space-like submanifolds of a Lorentzian space. In particular, we obtain a Bernstein rigidity theorem for complete minimal submanifolds of arbitrary codimension in Euclidean space.     

S~n中具Moebius平坦法丛的子流形

本文研究S~n中不含脐点、Moebius形式为零且具Moebius平坦法丛的子流形的Moebius特性。分别利用子流形的Moebius Ricci曲率与Blaschke张量、Moebius标准数量曲率以及Blaschke张量与Moebius标准数量曲率之间所满足的某种内蕴关系刻画了S~n中子流形的Moebius特性,得到了S~n中法丛平坦子流形的两个分类定理。     

四元数射影空间的全实伪脐子流形

本文给出了四元数射影空间中紧致全实伪脐子流形关于截面曲率和Ricci曲率的Pinching定理，并推广和改进了四元数射影空间中紧致全实极小流形的一些结果．     

The Fundamental and Rigidity Theorems for Pseudohermitian Submanifolds in the Heisenberg Groups

In this paper, we study some basic geometric properties of pseudohermitian submanifolds of the Heisenberg groups. In particular, we obtain the uniqueness and existence theorems, and some rigidity theorems.