理论数学

Vol.1 No.2 (July 2011)

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。

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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