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- Estimations of the moments of the hitting time by Brownian motions on general Riemannian manifolds are also obtained. 估计了一般黎曼流形上的布朗运动关于球面击中时的各阶矩。
- We generalizes the concept of the parallel rays of Euclidian space to a complete noncompact Riemannian manifolds and discuss its properties. 第二部分是讨论了黎曼流形中的一些几何问题，主要是将欧氏空间平行射线的概念推广到一般黎曼流形，并研究其所具有的性质。
- B. L. Chen and X. P. Zhu in [CZ] consider the Ricci flow on complete Riemannian manifolds and get a Bonnet-Myers type result. 进一步的通过考虑完备黎曼流形上的Ricci流，陈兵龙和朱熹平在文[CZ]中还得到了一个判断完备流形一定是紧致流形的Bonnet-Myers型定理。
- The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner. 对于黎曼流形的浸没建立了垂直能量泛函的二阶变分公式,研究强垂直调和映射的稳定性。
- The Laplacian on Riemannian manifolds is an essential linear operator, and it is also the main object to be studied of Geometric Analysis on manifolds. Riemann流形上的Laplace算子是一个重要的线性算子，也是流形上几何分析研究的主要对象之一。
- In this paper,the geometry of submanifolds with parally mean curvature vector in a locally symmetric, conformally falt Riemannian manifold is studied. 本文研究局部对称共形平坦黎曼流形中具有平行平均曲率向量的紧致子流形的性质。
- The auther worked out a pinching theorem of compact pesudoumbilical submanifolds with parallel mean curvature vector in a locally symmetric conformally flat Riemannian manifolds. 摘要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。
- In Riemannian manifolds, one studies Riemannian metric, covariant derivative, Riemannian connection, basic properties of the Riemann curvature tensor, curvature forms etc. 黎曼流形部分主要涉及黎曼度量，黎曼流形的定义，切向量场的协变微分，黎曼联络，黎曼几何的基本定理，曲率张量，曲率形式等概念和理论。
- This course should help students master definitions, basic peoperties and methods of differentiable and Riemannian manifolds, increase their ability from parts to a whole. 通过本课程的学习，希望学生能初步掌握微分流形的基本概念、方法和技巧，学习从局部到整体的数学技巧。
- This paper deals with the regular curves in a Riemannian manifold with constant sectional curvature and the affine starlike curves in R2, R3 and R4. 本文研究了具有常截面曲率的黎曼流形中的正则曲线及二、三、四维空间中的仿射星形曲线。
- This paper obtaines some pinching theorems of compactly minimal Submanifolds in a locally symmetric and conformal flat Riemannian manifold. 对局部对称共形平坦黎曼流形中具有平坦法丛的极小子流形作了一些讨论,得到了极小子流形是全测地的两个充分条件。
- At the most basic level, this course gives an introduction to the basic concepts of differential manifolds, exterior differentiation and Riemannian manifolds. 本课程主要介绍微分流形的基本概念和例子、外微分以及黎曼流形的初步知识。
- As an application, some nonexistence theorems of nonconstant stable harmonic maps from a Finsler manifold to a Riemannian manifold are given. 英文摘要： The first and second variation formulas of the energy functional for a nondegenerate map between Finsler manifolds is derived.
- In this paper,suppose M is a complete Riemannian manifold,and satifies dim HD( M) =1 ; then any harmonic m ap from M to a C-H manifold m ust be constant map was proved. 本文证明了完备非紧 Riemann流形 M;若其上不存在非常数、具有限 Dirichlet积分的调和函数 ;则从 M出发到任何 C-H流形的具有限能量的调和映照必为常值映照 .
- At the same time,The curvature tensor expression of a Riemannian manifold under the special semi-symmetric metric-recurrent connections is also obtained. 同时给出了特殊半对称联络的黎曼流形曲率张量表示。
- The n-dimensional umbilical submanifolds in a Riemannian manifold of quasi constant curvature are discussed. Two theorems on the above submanifolds are obtained. 摘要讨论拟常曲率黎曼流形中的全脐子流形，得到关于这类子流形的两个定理。
- Starting from the curvature of 3- dimensional Riemannian manifold, a new complex space which can contain the information of both geometrical optics and wave optics is built. 从三维黎曼流形的曲率出发，构造了一个复空间。它的流线能兼容几何光学与波动光学的信息。
- By the algebraic estimation to the Simons-Formula, a result of submanifolds with parallel mean curvature vector in a conformally flat Riemannian manifold is provided. 通过对共形平坦空间中的Simons公式的代数估计，得到其中具有平行平均曲率向量的紧致子流形的一个拼挤性质。
- 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. 摘要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。
- Abstract : In this paper,we study compact Riemannian manifolds which Ricci curvature ten-sors are parallel,and establish some pinching theorems for square of length of the Riemanniancurvatuer tensor. 摘要 ： 本文研究李奇曲率平行的封闭黎曼流形，证明了黎曼曲率平方的一个拚挤定理。
