VARIATIONAL PROPERTIES OF THE INTEGRATED MEAN CURVATURES OF TUBES IN SYMMETRIC SPACES

61. IntroductionLet P be a submanifold of an n-dimensional riemannian manifold AI. Expressions fOrthe kth integrated mean curvatures, M^P(t), (i. e. the integral of tho kth mcan curvature,k = 0, 1,' l n -- l), of a tubular hypersurface P of radius t about P, in terms of theRiemann curvature tensor of P. are calculated when AI is Euclidean or a rank one symmetricspace[5'13"1. Moreover, when P is a closed convex hypersurface of thc n-dimensional spaceof constant curvature A', Santal6 has…     

非负Ricci曲率开流形的拓扑

我们证明了对于具有非负Rieei曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C>0使得 则它微分同胚于欧式空间Rn.我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemarm流形微分同胚与Rn,改进了已知的结果.     

Liouville—Ttype Theorems for Conformal Gaussian Curvature Equations in R^2

In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions.     

振型归一化对梁结构柔度曲率损伤指标的影响

结构柔度矩阵需由质量矩阵归一化振型获得,而质量矩阵归一化振型难以直接测得,限制了柔度曲率类损伤指标的应用。为分析振型归一化方法对梁结构柔度曲率类损伤指标的影响,根据梁结构的刚度、弯矩和位移曲率的关系,建立了均布荷载作用下结构损伤前后位移曲率与损伤程度的理论表达式,实现定量分析均匀荷载面曲率结构损伤程度。提出P-范数振型归一化方法,通过均匀荷载面曲率指标推导了振型质量矩阵归一化系数差x_α与损伤程度的关系。以三跨连续梁算例对理论进行了验证,结果表明,损伤程度定量指标效果良好,不同P-范数振型归一化方法下,损伤程度的偏差可由2x_α估算;2-范数振型归一化方法的损伤识别结果与质量矩阵振型归一化结果最接近,故当无法获得质量矩阵归一化振型时,可采用2-范数归一化振型代替。     

活动标形及其在点啮合齿轮传动误差分析中的应用

活动标形法的论述首推苏步青译，佐佐木重夫著《微分几何学》，还有的著作从外微分形式引入活动标形,本文论证取曲面的正交曲率网为参数网时，曲面论的基本公式就是活动标形的微分形式，并用其分析了点啮合齿轮传动误差．     

一类Kähler 流形上的全纯映射

本文利用Kahler流形上的Laplace算子,给出了一类全纯映射的增长性结论.     

凸体的曲率映象与仿射表面积

本文研究了一些特殊凸体与其极体的曲率仿射表面积乘积的下界.对任意两个凸体,建立了它们的投影体的混合体积与其仿射表面积的一个不等式（见文[1-15]）.     

Horizontal Connection and Horizontal Mean Curvature in Carnot Groups

In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.     

具奇性广义平均曲率方程的径向对称解

本文研究具负指数奇性的广义平均曲率方程,在一个适当的且不可改进的条件下证明了径向对称古典解的存在唯一性.     

Rational Homotopy Theory and Nonnegative Curvature

in this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact non-negative curved manifolds admit （complete） metrics with non-negative curvature.