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Information Journal Paper

Title

Some rigidity results on complete Finsler manifolds

Pages

  100-117

Abstract

 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.

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