Azadeh Shirafkan - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran E-mail: ashirafkan@umz.ac.ir

Let F be a (reversible) Finsler metric on a Riemannian space (M, α) of positive (or negative) sectional curvature. Suppose that the Ricci curvature of F is horizontally constant along Finslerian geodesics. Then we show that F is a Ricci-quadratic Finsler metric.

Finsler space, Ricci-quadratic Finsler metric, H-curvature, Anisotropic space-time