Reversibility and Sub-reversibility of Finsler Metrics

In order to extend the sphere theorem for Finsler metrics, the concept of reversibil-ity introduced by H-B. Rademacher for a compact Finsler manifold. In this paper, weextend this notion to the general Finsler manifolds. Then we find an upper bound forthe reversibility of some important spherically symmetric Finsler metrics. Furthermore,we introduce the concept of sub-reversibility for a general Finsler manifold and obtain anon-zero lower bound for this new quantity.