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.
Asanjarani, A., & R. Dehkordi, H. (2022). Some rigidity results on complete Finsler manifolds. Journal of Finsler Geometry and its Applications, 3(1), 100-117. doi: 10.22098/jfga.2022.10415.1061
MLA
Azam Asanjarani; Hengameh R. Dehkordi. "Some rigidity results on complete Finsler manifolds". Journal of Finsler Geometry and its Applications, 3, 1, 2022, 100-117. doi: 10.22098/jfga.2022.10415.1061
HARVARD
Asanjarani, A., R. Dehkordi, H. (2022). 'Some rigidity results on complete Finsler manifolds', Journal of Finsler Geometry and its Applications, 3(1), pp. 100-117. doi: 10.22098/jfga.2022.10415.1061
VANCOUVER
Asanjarani, A., R. Dehkordi, H. Some rigidity results on complete Finsler manifolds. Journal of Finsler Geometry and its Applications, 2022; 3(1): 100-117. doi: 10.22098/jfga.2022.10415.1061
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