平行向量

平行向量场与Jacobi场的关系

The Relation between Parallel Vector Field and Jacobi Field

讨论了李群G上的左不变向量场、平行向量场与Jacobi场之间的关系，得到了G为平坦的一个充要条件。

In the paper , we discuss the relations among the left invariant vector field , the parallel vector field and the Jacobi field , get a sufficient and necessary condition for a Lie group to be flat .

复空间形式■~（2n）（C）中不存在平行平均曲率向量的紧致全实子流形

Compact totally real submanifolds in a complex space form without parallel mean curvature vector

DeSitter空间中具有平行平均曲率向量的完备类空子流形

Complete space-like submanifolds with parallel mean curvature vector in de Sitter spaces

关于具平行平均曲率向量场的三维紧致子流形的Ricci曲率的Pinching问题

On Pinching Problem of Ricci Curvature for 3-dimensional Compact Submanifolds with Parallel Mean Curvature

研究欧氏球面中具有平行平均曲率向量的紧致定向子流形，获得一个关于Ricci曲率满足处处大于或等于n-1+（n-1）H2+3n-2n（n-1）+2nHSn+1-nH2的条件下子流形的分类定理。

A closed oriented submanifold with parallel mean curvature vector field in a sphere is studied , and a Pinching theorem on the Ricci curvature of the submanifold is obtained .

设Mn是拟常曲率空间Nn+p中具有平行平均曲率向量的紧致伪脐子流形，论证得到了这种子流形的两个内蕴积分不等式，从而给出了Mn是全脐子流形的两个内蕴充分条件。

Let be a compact pseudo-umbilical submanifolds with parallel mean curvature vector in the quasi constant curvature space . Two integrate inequalities on this kind submanifolds are given , then two sufficient conditions for to be a totally umbilical submanifold in are given .

本文讨论了单位球面中具平行平均曲率向量的2－调和等距浸入，获得其成为极小浸入的充分条件和关于第二基本形式的Pinching定理。

In this paper , we discuss 2-harmonic isometric immersions in a sphere with parallel mean curvature vector . Conditions to become into a minimal immersion and pinching theorems on the second fundamental form are obtained .

CP~n中具有平行中曲率向量的全实子流形

Totally real submanifolds with parallel mean curvature vector in cp ~ n

球面中具平行平均曲率向量的子流形的一个整体特征

Global theorem of Submanifolds with parallel mean curvature in spheres

具有平行中曲率向量的子流形的一个积分不等式

An integral inequality for Submanifolds with parallel mean curvature vector

常曲率黎曼流形中具有平行中曲率向量的紧致伪脐子流形

The compact pseudo-umbilical submanifold with parallel mean curvature vector in the Riemannian manifold with constant curvature

对欧氏空间中的子流形M，若其法联络平坦，则存在平行的法向量场，由此可得与M平行的子流形M。

Let M be a Submanifold of Euclidean space with flat normal connection , then there exist parallel normal vector fields .

研究了拟常曲率流形中具有平行平均曲率向量的子流形，给出了两个积分不等式。

We study the submanifolds with parallel mean curvature vector in a manifold of quasi constant curvature , and give two integrate inequalities .

使得对拟常曲率黎曼流形中紧致子流形的研究由极小子流形和伪脐子流形情形扩展到具有平行平均曲率向量的情形。

The work makes the study of compact submanifolds in quasi constant curvature Riemannian manifolds extend from the especial case to general case .

研究局部对称共形平坦黎曼流形中具平行平均曲率向量的紧致伪脐子流形，得到了这类子流形模长平方的一个拼挤定理。

The auther worked out a pinching theorem of compact pesudoumbilical submanifolds with parallel mean curvature vector in a locally symmetric conformally flat Riemannian manifolds .

本文对一般拼挤黎曼流形中的具有平行平均曲率向量的等距浸入子流形给出了一个积分不等式，改进了已有的结果。

In this paper , we gave an integral inequality for isometric immersed submanifolds with Parallel mean curvature vector in pinched Riemannian manifolds , and improve the result obtained by H.Q.Xu .

研究单位球面上具有平行平均曲率向量的紧致子流形，得到了一个积分不等式和一个关于第二基本形式模长平方的拼挤定理。

This note deals with the compact minimal submanifolds in a unit sphere , the Laplaciano f the square of the length of the second fundamental form is calculated and estimated .

研究了局部对称黎曼流形中具有平行中曲率向量的子流形，给出了一个与子流形的截面曲率、平均曲率及余维数有关的夹挤定理。

The compact submanifolds with parallel mean curvature in locally symmetric δ - Pinching Riemannian manifold are discussed , a Pinching theorem for section curvature and mean curvature of submanifold is given .

给出了局部对称黎曼流行里具有平行中曲率向量的子流行的两个不等式，推广了邱成桐和莫小欢论文里相应的结果。

This paper provides two inequalities of the submanifold with parallel mean curvature vector in the locally symmetrical Riemannian manifold , and generalizes the two corresponding results of Yau S.T and Mo Xiao-huan .

讨论了拟常曲黎曼流形中具有平行平均曲率向量的等距浸入子流形，给出了一个积分不等式，推广和改进了文献[1,2]的结果。

In this paper , we study the isometric immersion submanifolds with parallel mean curvature vector in a Riemannian Manifold of quasi constant curvature , we also give an integral inequality , and improve the results in [ 1 ] 、 [ 2 ] .

获得了复射影空间中全实全脐子流形的若干性质，并且证明了复射影空间中具有平行平均曲率向量的正曲率紧致全实子流形必是伪脐的。

In this paper , some properties of totally real and totally umbilical submanifolds of a complex projective space are obtained . We also prove that a compact totally real submanifold with positive curvature and parallel mean curvature vector of a complex projective space must be pseudo-umbilical .

局部对称共形平坦Riemann流形中具有平行单位中曲率向量的子流形

The Submanifold with Parallel Mean Curvature in Local Symmetric Plat Riemann Manifold

具有平行正则平均曲率向量的稳定子流形

On stationary Submanifolds with parallel normalized mean curvature vector

本文第一章研究具有常数数量曲率和平行单位平均曲率向量场的子流形。

In the first chapter of the paper , we study the case that Mn is a submanifold in a unit sphere Sn + p with constant normalized scalar curvature and parallel normalized mean curvature vector field .