具非负曲率的完备非紧黎曼流形  

Complete Non-Compact Riemannian Manifold with Nonnegative Curvature

作　　者：詹华税[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《厦门大学学报（自然科学版）》2006年第6期756-758,共3页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10571144);福建省教育厅基金(JA05296);集美大学预研基金资助

摘　　要：将三维欧式空间旋转抛物面顶点的定义推广到一般的非负曲率完备非紧黎曼流形上,利用Perelman G证明Chee-ger-Gromoll核心猜想的几何方法,讨论了具非负曲率的完备非紧黎曼流形M上的核心S的结构,证明了如果由核心出发的法测地线均为射线,则或者S退化为一点,或者M=Rk×N,其中N是紧致的具非负曲率的黎曼流形.特别地,如果核心的维数仅比流形的维数低一维,可以证明其法测地线均为射线,从而有M=Rn-1×S.It is well-known that there is a unique vertex on rotating parabolic surface in three-dimensional Euclidiean space, the paper generalizes the concept of vertex to a complete noncompact Riemannian manifold with nonnegative curvature. By the geometric method used by Perelmann G in his well-known paper in which Cheeger-Gromoll conjecture was solved, the paper discusses the structure of the soul in a complete noncompaet Riemannian manifold M with nonnegative curvature, proves that if the normal geodes- ics from soul are rays in M, then either M is diffeomorphic to R＊ or M= R^k×N. Where N is a compact manifold with nonnegative curvature. In particular, if dimS= dimN-1,the paper proves that every normal geodesic from S is a ray in M, thus M=R^n-1 × S.

关 键 词：完备非紧黎曼流形 非负曲率 核心 极点 

分 类 号：O186.12[理学—数学]