A Strong Rigidity Result on Complete Finsler Manifolds via a Second Order Differential Equation
2020
We provide an extension of the Obata's theorem to Finsler geometry and establish some rigidity results based on a second order differential equation. Mainly, we prove that: Every complete connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to an Euclidean sphere endowed with a certain Finsler metric and vice versa.
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