黎曼流形上的幂零结构指什么？
设m是紧致连通的黎曼流形。
黎曼流形运动群的研究是微分几何中一个重要问题。
Research of the group of motions in Riemann manifold is an important question of the differential geometry.
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。
Estimations of the moments of the hitting time by Brownian motions on general Riemannian manifolds are also obtained.
研究拟常曲率黎曼流形中具有平行平均曲率向量的紧致子流形。
The compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied.
在黎曼流形上分别给出了伪不变凸函数和弱向量似变分不等式的概念。
The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.
并由此讨论了紧致的非单连通黎曼流形上无穷多的闭测地线存在性问题。
Also, the paper discuss the existence of the infinite closed geodesics of a compact no-simply connected Riemannian manifold.
讨论特殊半对称联络的黎曼流形，给出了该流形曲率张量的一个代数结构。
In the present paper, the algebra property of Riemannian manifold which is contained some special semi symmetric connection is given.
本文讨论黎曼流形里一般余维的常数平均曲率的子流形为全脐子流形的充要条件。
In this paper, we get a necessary and sufficient condition for a generalcodimensional submanifold with constant mean curvature in a Riemannian mani-fold to be a totally umbilical submanifold.
爱因斯坦流形是特殊的一种黎曼流形，它有很好的特征，其定义弱于常曲率黎曼流形。
Einstein manifold is a particular kind of Riemannian manifold, it has good characters, its definition is weaker than Riemannian manifold with constant sectional curvature.
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 second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner.
李三系作为一种代数体系，最初源于对黎曼流形的一类特殊子空间——全测地子流形的研究。
As an algebraic system, Lie triple systems arise upon consideration of certain sub-spaces of Riemannian manifolds, the totally geodesic submanifolds.
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.
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。
This paper studies the Schouten tensor on the locally conformally flat manifold, and gets some sufficient conditions for m to be the space of constant curvature, which improves the known results.
利用黎曼对称空间同正交对称李代数之间的密切关系及一个矩阵不等式给出了一个复流形上截面曲率的上界的精确估计。
We used the relationship of the Riemann symmetric space and the symmetric algebra, a matrix inequality to provided a estimate sectional curvature of a complex manifold.
本文研究了伪黎曼空间型中具有常平均曲率的类空子流形，得到了这类空子流形的一个积分不等式及刚性定理。
This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form, and obtain an integrate inequality and a rigidity theorem.
它进一步说明一个四元流形的截面曲率的估计对许多对称黎曼空间都是有效的。
It proves that the estimate sectional curvature of a quaternion manifold is very useful for Riemann symmetric space.
通过计算全测地子流形的基本群，确定了紧正规黎曼对称空间的极大的极大秩全测地子流形的整体分类。
In this paper, the authors give the globally classfication of the maximal totally geodesic submanifolds with maximal rank of normal Riemannian symmetric Spaces by computing the fundamental group.
通过计算全测地子流形的基本群，确定了紧正规黎曼对称空间的极大的极大秩全测地子流形的整体分类。
In this paper, the authors give the globally classfication of the maximal totally geodesic submanifolds with maximal rank of normal Riemannian symmetric Spaces by computing the fundamental group.
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