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The ideal boundaries and global geometric properties of complete open surfaces

Published online by Cambridge University Press:  22 January 2016

Takashi Shioya
Takashi Shioya*
Affiliation:
Department of Mathematics, Faculty of Science, Fukuoka 812, Japan
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 120 , December 1990 , pp. 181 - 204
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

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