What is nilpotent structure on Riemannian manifold?
黎曼流形上的幂零结构指什么？
Let m be a compact and connected Riemannian manifold.
设m是紧致连通的黎曼流形。
Positive curvature has been a frequent subject in Riemannian geometry.
曲率是黎曼几何中的热门研究课题。
The dynamic problem of constrained multibody systems in Riemannian configuration space is researched.
在黎曼位形空间中研究了约束多体系统的动力学问题。
In this paper, we focus on these three problems and extend first two problems to Riemannian manifolds.
本文主要对上述三个问题进行较为深入的研究，并把前两个问题推广到黎曼流行上。
A method based on Riemannian metric to the classification problem with imbalanced training data was proposed.
本文提出一种基于黎曼度量的训练样本类不平衡问题的分类方法。
In this paper, a possible Correction of non-Riemannian geometric relativity is made for Newton's Law of Gravitation.
本文对牛顿万有引力定律提出了一种非黎曼几何的相对论性的可能修正公式。
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。
In the end, the problem of robot trajectory planning is investigated by the linearization method and Riemannian metric.
最后，应用近似化方法和黎曼度量方法，研究了机器人最优轨迹规划的问题。
The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.
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 compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied.
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。
Also, the paper discuss the existence of the infinite closed geodesics of a compact no-simply connected Riemannian manifold.
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。
In this paper, we present a lower bound for the first eigenvalue of the total Spaces of some class of Riemannian submersions.
给出了一类黎曼浸没在全空间中第一特征值的下界估计。
In the present paper, the algebra property of Riemannian manifold which is contained some special semi symmetric connection is given.
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。
These results are in agreement with those obtained by general relativity expressed in Riemannian geometry and that from practical observations.
结果与用黎曼几何表述的广义相对论和实际观测相符。
The work makes the study of compact submanifolds in quasi constant curvature Riemannian manifolds extend from the especial case to general case.
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 paper gives a simple version and progress of the open Riemannian manifolds with nonnegative Ricci curvature and large volume growth from 1990.
在本文中，我们主要研究具有非负曲率完备非紧流形的体积增长与闭测地线及距离函数临界点一些关系。
Under a suitable condition, this paper gives an existence theorem for harmonic maps from surfaces to certain Riemannian manifolds in a large scale.
在一定条件下，给出了一个从曲面出发的大范围调和映照的存在性定理。
As an algebraic system, Lie triple systems arise upon consideration of certain sub-spaces of Riemannian manifolds, the totally geodesic submanifolds.
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。
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。
One novel gaze point compensation algorithm in Riemannian space was proposed in this paper based on the estimation algorithm of gaze point in space similar triangles.
在空间相似三角形注视点估计算法的基础上，提出一种基于黎曼几何的视线落点补偿方法 。
Einstein manifold is a particular kind of Riemannian manifold, it has good characters, its definition is weaker than Riemannian manifold with constant sectional curvature.
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。
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.
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 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。
Rotation hypersurfaces in pseudo-Riemannian space forms are defined and their explicit parametrizations are given in the present paper, and their principal curvatures are computed.
本文定义了伪黎曼空间型中的旋转超曲面，并给出其参数表达式及主曲率计算公式。
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.
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, 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.
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。
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