A proof of Toponogov's theorem in Alexandrov geometry
Differential Geometry
2022-03-29 v1 Metric Geometry
Abstract
This paper aims to give an elementary proof for Toponogov's theorem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian geometry, sectional curvature can be embodied in the second variation formula.
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Cite
@article{arxiv.2203.14626,
title = {A proof of Toponogov's theorem in Alexandrov geometry},
author = {Shengqi Hu and Xiaole Su and Yusheng Wang},
journal= {arXiv preprint arXiv:2203.14626},
year = {2022}
}
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5 pages