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 :;

关键词: 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

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。

Abstract:
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.

文章引用: 詹华税 (2011) 完备非紧黎曼流形上的射线的平行性。 理论数学, 1, 159-162. doi: 10.12677/pm.2011.12031

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