Hassan Sadeghi - Department of Mathematics, Faculty of Science, University of Qom, Qom. Iran. E-mail: sadeghihassan۶۴@gmail.com

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.

Finsler geodesic, S-curvature, Landsberg curvature