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黎曼流形上的幂零结构指什么？What is nilpotent structure on Riemannian manifold?

设M是紧致连通的黎曼流形。Let M be a compact and connected Riemannian manifold.

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设R和S为两个超越椭圆黎曼曲面。Let R and S be transcendental elliptic Riemannian surfaces.

曲率是黎曼几何中的热门研究课题。Positive curvature has been a frequent subject in Riemannian geometry.

通过得到的惯性矩阵，应用黎曼曲率有效地分析了机器人动力学操作性能。Through using the inertial matrix, we analyse the manipulation of robot by the Riemannian curvature.

在黎曼位形空间中研究了约束多体系统的动力学问题。The dynamic problem of constrained multibody systems in Riemannian configuration space is researched.

HCMU度量是黎曼曲面上极值度量的一个退化情形，具有整体旋转对称性。HCMU metric is a special kind of extremal metric on Riemannian surface with global rotational symmetric.

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利用黎曼几何等工具研究了一般并联机器人的动力学建模和跟踪控制的一般化方法。Using the Riemannian geometry language, the modeling and control of general parallel robots are studied.

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.

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。In the end, the problem of robot trajectory planning is investigated by the linearization method and Riemannian metric.

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.

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.

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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.

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 this paper, we present a lower bound for the first eigenvalue of the total spaces of some class of Riemannian submersions.

讨论了非紧对称空间平方可积微分形式的离散序列，并给出其离散谱的一个具体描述。This paper discusses the discrete series of the L 2 integrable differential forms for noncompact Riemannian symmetric spaces.

建立了从欧氏空间到任何黎曼流形的具有有限F-能量的F-调和映照的非存在性定理。A nonexistence theorem is established for F-harmonic map with finite F-energy from Euclidean space to any Riemannian manifold.

结果与用黎曼几何表述的广义相对论和实际观测相符。These results are in agreement with those obtained by general relativity expressed in Riemannian geometry and that from practical observations.

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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.

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。The paper gives a simple version and progress of the open Riemannian manifolds with nonnegative Ricci curvature and large volume growth from 1990.

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.