A lower bound for total curvature of a closed curve in a cat(K) space

A. Sama-AeW. KharuwannapatC. ManeesawarngPrince of Songkla UniversityThaksin UniversityMahidol UniversitySouth Carolina Commission on Higher Education2018-06-112018-06-112012-11-01JP Journal of Geometry and Topology. Vol.12, No.3 (2012), 243-2620972415X2-s2.0-84872001802https://repository.li.mahidol.ac.th/handle/20.500.14594/14392A lower bound for total curvature of a closed curve in a metric space of nonzero curvature in the sense of Alexandrov is investigated in this A. Sama-Ae, W. Kharuwannapat and C. Maneesawarng paper. We find that the total curvature of a closed curve 2π in case of K < 0, and is more than or qual to case of K > 0, where its perimeter Our results extend some well-known facts proved by Tsukamoto [1© 2012 Pushpa Publishing House.Mahidol UniversityMathematicsA lower bound for total curvature of a closed curve in a cat(K) spaceArticleSCOPUS