The ideal boundaries and global geometric properties of complete open surfaces
The ideal boundaries and global geometric properties of complete open surfaces
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完全开放曲面的理想边界和全局几何特性
DOI：
10.1017/s0027763000003330
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发表时间：
1990
影响因子：
0.8
通讯作者：
T. Shioya
中科院分区：
文献类型：
--
作者：
T. Shioya
本文研究了作为[Sy2]和[Sy3]的延拓的具有全曲率曲面的理想边界。阿达玛流形的理想边界被定义为射线的等价类。这个等价关系是由Busemann [Bu]定义的射线的渐近关系。渐近关系一般是非对称的。然而在阿达玛流形中，这是对称的。这里重要的是流形是无焦点的。
In this paper we study the ideal boundaries of surfaces admitting total curvature as a continuation of [Sy2] and [Sy3]. The ideal boundary of an Hadamard manifold is defined to be the equivalence classes of rays. This equivalence relation is the asymptotic relation of rays, defined by Busemann [Bu]. The asymptotic relation is not symmetric in general. However in Hadamard manifolds this becomes symmetric. Here it is essential that the manifolds are focal point free.