Abstract

In this paper, we prove the Frankel's refinement of Bochner's theorem on both compact and forward complete Finsler manifolds. That is, on a compact or forward complete Finsler manifold M0 with non-positive flag curvature and negative (mean) Ricci curvature, any isometry ψ:M0→M0 homotopic to the identity must be the identity itself.

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