非负曲率的完备黎曼流形上的平行射线
The Parallelism of the Rays in a Complete Riemannian Manifold with Nonnegative Curvature
摘要
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.同时证明了具完全平行性质的非负曲率的完备非紧黎曼流形M=Rk×S,其中S为核心. 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.Wu.Moreover,M=R~k×S is provided whereM is the complete parallel properties andS is the soul ofM.