%0 Journal Article
%T Some rigidity results on complete Finsler manifolds
%J Journal of Finsler Geometry and its Applications
%I University of Mohaghegh Ardabili
%Z 2783-0500
%A Asanjarani, Azam
%A R. Dehkordi, Hengameh
%D 2022
%\ 07/01/2022
%V 3
%N 1
%P 100-117
%! Some rigidity results on complete Finsler manifolds
%K Finsler metric
%K Rigidity
%K Constant curvature
%K Second-order differential equation
%K Adapted coordinate
%R 10.22098/jfga.2022.10415.1061
%X We 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.
%U https://jfga.uma.ac.ir/article_1671_16df84e3513a82e16e6237882007ccd7.pdf