Abstract

For a non-reversible Finsler metric F on a compact smooth manifold M we introduce the reversibility λ= max {F(−X)|F(X)=1}≥1. We prove the following generalization of the classical sphere theorem in Riemannian geometry: A simply-connected and compact Finsler manifold of dimension n≥3 with reversibility λ and with flag curvature \({{{{\left({{1-\frac{{1}}{{1+\lambda}}}}\right)}}^2 < K \le 1}}\) is homotopy equivalent to the n-sphere.

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