TY - JOUR
T1 - Applications of Toponogov's comparison theorems for open triangles
AU - Kondo, Kei
AU - Tanaka, Minoru
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:84879302872
VL - 50
SP - 541
EP - 562
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
SN - 0030-6126
IS - 2
ER -