On a class of Ricci-quadratic Finsler metrics

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.

Keywords:

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