Reversibility and Sub-reversibility of Finsler Metrics

Document Type : Original Article


Department of Mathematics, Faculty of Science, University of Qom Qom. Iran


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, we
extend this notion to the general Finsler manifolds. Then we find an upper bound for
the reversibility of some important spherically symmetric Finsler metrics. Furthermore,
we introduce the concept of sub-reversibility for a general Finsler manifold and obtain a
non-zero lower bound for this new quantity.