Applications of Toponogov's comparison theorems for open triangles

Kei Kondo, Minoru Tanaka

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)541-562
Number of pages22
JournalOsaka Journal of Mathematics
Volume50
Issue number2
Publication statusPublished - Jun 2013
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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