曲率

In chapter 4,we consider the existence of harmonic function in negative sectional curvature manifolds.we get that,if Ricci ≥-C(1 + r~2)r =ρ(O.x, then there have non-canstant bounded harmnic function in negative sectional curvature manifolds.

第四章考虑负曲率流形上调和函数，得到了在Ricci≥-C(1+r~2)其中r=ρ的负曲率流形的调和函数的存在性。

Theorem 4 There is no compact totally real 2-harmonic submanifold with non-zero parallel mean curvature and positive sectional curvature in a locally symmetric Bochner -Kaehler manifold.

定理4局部对称Bochner-Kaehler流形中不存在具有非零平行平均曲率向量且截面曲率大于零的紧致全实2-调和子流形。

Theorem 3 Let M~n be a compact totally real 2-harmonic submanifold in M~n which is a locally symmetric Bochner-Kaehler manifold.If Ricci curvature of M~n is nonegative and positive at a point at least,then the holomorphic sectional curvature of M~n is a postive constant number.

定理3设M~n是局部对称Bochner-Kaehler流形M~n的紧致全实2-调和子流形，若M~n的Ricci曲率非负且至少在一点为正，则M~n具有正常数全纯截面曲率。

During the process, following were considered:the effects of variable radius of cross section on the vertical bending deflection angle, noncoincidence of torsional center and gravity center, the effect of transverse shearing strain on energy of strain.

推导中除考虑曲率变化、截面形心和剪切中心分离、梁的横向剪切变形影响等因素外，还考虑了曲率沿横向变化对竖向挠转角的影响。

High-precision spherical components have been widely used in precision machinery and aerospace industry, and spherical curvature is one of determinant to the capability of optical components, and the measure of it is an important matter in the optical component manufacture. So the research of the high precision measurement of spherical curvature has important significance.

中文摘要高精度球面元件在精密机械和航天工业中的应用越来越广泛，在光学生产的加工制造过程中也大量需要对具有球面形状的透镜的曲率半径进行高精密测量的情况，因此，球面元件曲率半径的精密测量对高质量球面样板，光学系统的质量控制等方面具有重要的意义。

The curvature radius of optical sphere is an important parameter to determine the properties of an optical sphere. The measurement result of the spherical curvature radius can be used to assess the quality of an optical component.

光学球面曲率半径是决定光学球面光学特性的重要参量，通过测量光学球面的曲率半径，可以审核光学元件设计制造质量。

In this thesis, several kinds of spherical curvature measurement methods are introduced, and the "arch-high and chord-length method" is selected after introduction of the existing methods, and then the novel type of instrument for measuring spherical curvature with the variable ring is developed. In research, the grating sensor, integrated circuits and other new technologies are adopted and integrated. As a result of this, Its specific technical indicator is 0.1um in absolute accuracy, 0.01% in relative accuracy, and 0.001% in repeat accuracy.

本文首先对几种球面曲率半径的测量系统进行了深入的理论分析，在分析了各个测量方法优缺点的基础上，选用了"弓高弦长法"的测量原理，并从理论上推导了本文所述系统的可行性，采用光栅传感器、集成电路等新技术成果，将机械、电子技术、计算机技术以及传感器技术有机结合，研制出一种新型的可变径球面曲率测量仪器。

By using curvature analysis, the exact calculation of tracing direction and the estimation of tracing step length are given.

本文总结了用平面向量场确定初始跟踪点的算法，介绍了Kriezis的方法，指出了法曲率与跟踪方向的关系，并给出用曲率分析方法精确计算跟踪方向、估计跟踪步长的算法。

In the third chapter, we study complete minimal submanifolds of locallysymmetric space, and we obtain a pinching theorem about the Ricci curvature of the minimal submanifolds, which generalizes the result of Norio Ejiri\'s from sphere space to locally symmetric space.

第三章节研究局部对称空间中具有正Ricci曲率的完备极小子流形，得到了关于子流形Ricci曲率的一个pinching定理，该定理把Norio Ejiri的结论从外围空间为球空间推广到局部对称空间中。

Moreover, if M~n is strongly stable and has finite total curvature, then M~n is an affine n-plane.

第二，我们研究了欧氏空间R~(n+1)和双曲空间H~(n+1)(-1)中具有常平均曲率H及有限L~p范数曲率的完备超曲面。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。