Applications of Toponogov's comparison theorems for open triangles
Abstract
Recently we generalized Toponogov's comparison theorem to a complete Riemannian manifold with smooth convex boundary, where a geodesic triangle was replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface was replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary. The aim of this article is to prove splitting theorems of two types as an application. Moreover, we establish a weaker version of our Toponogov comparison theorem for open triangles, because the weaker version is quite enough to prove one of the splitting theorems.
Keywords
Cite
@article{arxiv.1102.4156,
title = {Applications of Toponogov's comparison theorems for open triangles},
author = {Kei Kondo and Minoru Tanaka},
journal= {arXiv preprint arXiv:1102.4156},
year = {2013}
}
Comments
This article is a version split from our article "Toponogov comparison theorem for open triangles" (arXiv:0905.3236) to submit to a journal. 19 pages, no figures