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- 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 .
- 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 Parallelism of the Rays in a Complete Riemannian Manifold with Nonnegative Curvature 非负曲率的完备黎曼流形上的平行射线
- Maximal and Minimal Value Principle of Differentiable Functions on Noncompact Complete Riemannian Manifold 非紧完备黎曼流形上可微函数的极值原理
- The Properties of the Soul in a Complete Riemannian Manifold with Nonnegative Curvature 具非负曲率的完备黎曼流形上核心的性质
- complete Riemannian manifold 完备黎曼流形
- 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。
- 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。
- 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.
- complete noncompact Riemannian manifold 完备非紧黎曼流形
- 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。
- normal complete open riemannian manifold 完备非紧正则黎曼流形
- 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。
- Let Nn+p(c)be an n+p dimensional Riemannian manifold with constant curvature c and Mn an n dimensional compact submanifold of Nn+p(c). It is known that there is a Simons'inequality when Mn is minimal. 设Mn是等距浸入在常曲率黎曼流形Nn+p(c)中的n维紧致子流形;若Mn是极小的;有著名的Simons不等式.
- ZHANG Jian-feng.On submanifolds with parallel mean curvature vector in a locally symmetric conformally flat Riemannian manifold [J].J of Zhejiang University (Science Edition), 1999,26(4) :26-34. [9]张剑锋.;局部对称共形平坦黎曼流形中具有平行平均曲率向量的子流形[J]
- The uses of this machine are manifold. 这台机器有多种用途。