A Schur-Toponogov theorem in Riemannian geometry & a new proof of Toponogov's theorem in Alexandrov geometry

2018/09/26 by Wang, Yusheng
#53-C20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.09818

Abstract

In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem (in the large) in Alexandrov geometry.

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