刚性定理

In this paper, by computing the Laplace of the square of the length of the second fundamental form and introducing a self-adjoint operator and using Stokes Theorem and Hopf Theorem, we obtained some pinching theorems and rigidity theorems for hypersurfaces and submanifolds in hyperbolic space.

本论文通过计算双曲空间中子流形的第二基本形式模长平方的拉普拉斯和引进一个新的自共轭二阶算子，利用Stokes定理和Hopf定理得到了子流形的一些拼挤定理和刚性定理。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

In this article,we mainly study the space-like submanifolds with parallel mean curva-ture vector,constant scalar curvature or constant square length of the second fundamental form,respectively.We obtain some pinching theorems and rigidity results by estimating Laplace of the square length of the second fundamental form of the such submanifolds and using yaus maximum principle or Stokes Theorem.

本论文主要研究de Sitter空间中具有平行平均曲率向量、常数量曲率或第二基本形式模长平方是常数的三类类空子流形，并通过分别估计三种情形下子流形的第二基本形式模长平方的Laplace，利用Yau的极大值原理和Stokes定理，获得了这些子流形的一些拼挤定理和刚性定理。

In this thesis, we mainly study several problems on geometry and topology of Rieman-nian submanifolds, which contains the geometric rigidity, topological sphere theorems and eigenvalue problems of Laplace-Beltrami operator on Riemannian submanifolds.

本文着重研究黎曼子流形上几何与拓扑的若干问题，主要内容包括子流形的几何刚性、拓扑球面定理和Laplace-Beltrami算子的特征值问题。

A bending motion equation of a tilting drive shaft with rigid multi-supports is derived by theorem of the motion of mass center, method of Galerkin and Heaviside function.

根据质心运动定理、Galerkin法和Heaviside函数，求得非惯性系下倾斜刚性多支点传动轴的弯曲运动方程。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。