Abstract
It is shown that a Finsler metric with positive constant flag curvature and vanishing mean tangent curvature must be Riemannian. As applications, we also discuss the case of Cheng's maximal diameter theorem and Green's maximal conjugate radius theorem in Finsler manifolds.
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Kim, Cw., Yim, Jw. Finsler Manifolds with Positive Constant Flag Curvature. Geometriae Dedicata 98, 47–56 (2003). https://doi.org/10.1023/A:1024034012734
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DOI: https://doi.org/10.1023/A:1024034012734