Pythagorean Theorem & Curvature with Lower or Upper Bound*

Citation:

Yusheng WANG.Pythagorean Theorem & Curvature with Lower or Upper Bound*[J].Chinese Annals of Mathematics B,2022,43(1):95~114
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Authors:

Yusheng WANG;

Foundation:

National Natural Science Foundation of China (No. 11971057) and BNSF Z190003.
Abstract: In this paper, the authors give a comparison version of Pythagorean theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).

Keywords:

Pythagorean theorem, Alexandrov space, Toponogov’s theorem

Classification:

53C20
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