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 Δ2f = −kfgΔf for a positive constant k, then M is diffeomorphic with the n-sphere 𝕊n, 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.