A Note on Finsler Version of Ambrose Theorem

Abstract

Let (ℵ,𝐹�) be a forward complete and connected Finsler manifold of dimensional 𝑛�≥2. In this study, we extend Ambrose’s compactness theorem in Riemannian manifolds to Finsler manifolds by using the weighted Ricci curvature. We use the Bochner Weitzenböck formula and suitable sequence choices for the proofs of the desired results.