A special class of Finsler metrics

In this paper, we study a special class of Finsler metrics F = F(x, y) in Rn that satisfy F(−x, y) = F(x, y). We show the induced distance function of F satisfies dF (p, q) = dF (−q,−p) for all p, q in Rn. The geodesics of these metrics have special property and many well-known Finsler metrics belong to this class. We prove that these metrics with constant S-curvature satisfy S = ۰.

Keywords:

Finsler geodesic , S-curvature , Landsberg curvature