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C-Totally Real Submanifolds with parallel mean curvature vector of Sasakian Space Form

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Journal of Mathematical Research and Exposition 2002年第4期22卷 545-548页

作者：宣满友刘继志绍兴文理学院数学系浙江绍兴312000 北京师范大学数学系北京为100875

We have discussed the C-totally real subrnanifolds with parallel mean curvature vector of Sasakian space form, obtained a formula of *** type, and improved one result of ***.

关键词： Sasakian space form parallel mean curvature vector C-totally real sub-manifold.

The Submanifolds with parallel mean curvature vector in a Locally Symmetric and Conformally Flat Riemannian Manifold

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Chinese Quarterly Journal of Mathematics 1992年第1期7卷 32-36页

作者：孙华飞东北工学院数学系沈阳110006

In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M... 详细信息

关键词： Locally symmetric conformally flat parallel mean curvature vector

A complete classification of Blaschke parallel submanifolds with vanishing Mbius form

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Science China Mathematics 2017年第7期60卷 1281-1310页

作者： LI XingXiao SONG HongRu College of Mathematics and Information Science Henan Normal University Xinxiang 453007 China

The Blaschke tensor and the Mbius form are two of the fundamental invariants in the Mobius geometry of submanifolds;an umbilic-free immersed submanifold in real space forms is called Blaschke parallel if its Blaschke tensor is *** prove a theorem which,together with the known classification result for Mobius isotropic submanifolds,successfully establishes a complete classification of the Blaschke parallel submanifolds in S^n with vanishing Mobius *** doing so,a broad class of new examples of general codimensions is explicitly constructed.

关键词： parallel Blaschke tensor vanishing Mobius form constant scalar curvature parallel mean curvature vector

Proper Biharmonic Submanifolds in a Sphere

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Acta Mathematica Sinica,English Series 2012年第1期28卷 205-218页

作者： Xian Feng WANG Lan WU School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071P.R.China Department of Mathematics Renmin University of ChinaBeijing 100872P.R.China

In this paper, we obtain a constraint of the mean curvature for proper biharmonic submanifolds in a sphere. We give some characterizations of some proper biharmonic submanifolds with parallel mean curvature vector in ... 详细信息

关键词： Proper biharmonic map parallel mean curvature vector mean curvature

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伪球面上具有平行平均曲率向量场的子流形

杭州大学学报(自然科学版) 1986年第2期 129-135页

作者：郭孝英

1.设Hn+p是一个具有常数截面曲率-1的,n+p维伪球面.如所周知,Hn+p中不存在任何紧致极小子流形.考虑Hn+p中具有平行平均曲率向量场ξ的n维紧致子流形Mn,沈一兵最近得到这种Mn是全脐点的关于截面曲率的充分条件.本文考虑这种Mn的Ricci曲... 详细信息

1.设Hn+p是一个具有常数截面曲率-1的,n+p维伪球面.如所周知,Hn+p中不存在任何紧致极小子流形.考虑Hn+p中具有平行平均曲率向量场ξ的n维紧致子流形Mn,沈一兵最近得到这种Mn是全脐点的关于截面曲率的充分条件.本文考虑这种Mn的Ricci曲率的限制条件,证得:若Mn的截面曲率为正,并且Mn的Ricci曲率处处不小于μ（‖ξ‖2-1）,其中μ=n-2（n≥4）或μ=5/4（n=3）,则Mn是Hn+p中某个n+1维全测地子流形Hn+1的全脐点超曲面.此外,我们也得到了关于数量曲率与截面曲率的某些积分不等式.

关键词： Submanifold pseudo-sphere parallel mean curvature vector compact submanifold

On Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space

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Journal of Mathematical Research and Exposition 2008年第2期28卷 421-428页

作者： ZHANG Liang College of Mathematics and Computer Science Anhui Normal University Anhui 241000 China

Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal *** choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.

关键词： complex projective space totally real submanifolds pseudo-umbilical submanifolds parallel mean curvature vector