University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003120220701Some rigidity results on complete Finsler manifolds100117167110.22098/jfga.2022.10415.1061ENAzam AsanjaraniDepartment of Statistics, The University of Auckland, Auckland, New Zealand0000-0001-6115-073XHengameh R. DehkordiCenter of Mathematics, Computing and Cognition - CMCC
Federal University of ABC - UFABC, SP, Brazil.Journal Article20220223We provide an extension of Obata's theorem to Finsler geometry and establish some rigidity results based on a second-order differential equation. Mainly, we prove that every complete simply connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to a Euclidean sphere endowed with a certain Finsler metric and vice versa. Based on these results, we present a classification of Finsler manifolds which admit a transnormal function. Specifically, we show that if a complete Finsler manifold admits a transnormal function with exactly two critical points, then it is homeomorphic to a sphere.https://jfga.uma.ac.ir/article_1671_16df84e3513a82e16e6237882007ccd7.pdf