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詹华税. 具有完全平行性质和非负曲率的完备黎曼流形[J]. 厦门大学学报(自), 2003, 73(43): 441-443.

被以下文章引用:

• 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.