Certain Conditions for a Finsler Manifold to Be Isometric with a Finsler Sphere

Abstract

Abstract We show that if there is a smooth function f on a Finsler n -space M satisfying Δ2 f = − kfg Δ f for a positive constant k , then M is diffeomorphic with the n -sphere 𝕊 n , where g denotes the weighted Riemannian metric. Moreover, we further show that the manifold is isometric to a Finsler sphere if the Ricci curvature is bounded below by ( n − [one.tf]) k and the S -curvature vanishes.