Projectively Ricci-flat general (?, ?)-metrics

Abstract

In this paper, we study the projectively Ricci-flat general (alpha, beta)-metrics within to a spray framework and also bring out the rich variety of behaviour displayed by an important projective invariant. Projective Ricci curvature is one of the essential projective invariant in Finsler geometry which has been introduced by Z. Shen. The projective Ricci curvature is defined as Ricci curvature of a projective spray associated with a given spray G on M-n with a volume form dV on M-n.