标题:
完备非紧黎曼流形上的射线的平行性The Parallelism of the Rays in a Complete Noncompact Riemannian Manifold
作者:
詹华税
关键字:
平行射线, Busemann函数, 完全平行性质, Wu-Chen问题Parallel Rays; Busemann Function; Complete Parallel Property; Wu-Chen Problem
期刊名称:
《Pure Mathematics》, Vol.1 No.2, 2011-08-09
摘要:
将欧式空间平行射线的概念推广到一般完备非紧的黎曼流形上,证明了只有符号相反的Busemann函数的完备非紧的黎曼流形具有完全平行性质。部分地回答了Wu-Chen问题。The paper generalizes the concept of the parallelism for the rays in Eucliden space to a general noncompact Riemannian manifold, proves that if the manifold has only two Busemann function with adverse signs, then the manifold is with complete parallel property. This conclusion answers Wu-Chen Problem partly.