Pythagorean Theorem & curvature with lower or upper bound

2019/11/04 by Su, Xiaole, Sun, Hongwei, Wang, Yusheng
#53C20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1911.01019

Abstract

In this paper, we give a comparison version of Pythagorean Theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).

Related

• Alexandrov geometry: foundations
• New definitions of Alexandrov space and applications
• A proof of Toponogov's theorem in Alexandrov geometry
• A rigidity theorem in Alexandrov spaces with lower curvature bound
• Isoperimetric characterization of upper curvature bounds