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.
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。
The paper discusses the structure of the soul in a complete noncompact Riemannian manifold M with nonnegative curvature,and proves that if the soul of the manifold is unique,then the soul actually degenerates to a pole.
讨论了具非负曲率的完备非紧黎曼流形上的核心的结构,证明了如果核心是惟一的,那么核心将退化为极点。
The parallel properties of the rays in a complete noncompact Riemannian manifoldM were discussed in this paper, It is proved that the Busemann functions corresponding to any given two parallel rays are just the same as each other in the sense of H.
讨论了具非负典率的完备非紧黎曼流形M上平行射线的性质,证明了此时两平行射线对应于M上的同一个Busemann函数。