On Ricci Tensors of a Finsler Space with Special (α, β)−Metric

Abstract

In the present paper, we find the Ricci tensor of a Finsler space of a special (α, β)-metric F = µ_1 α + µ_2 β + µ_3 β^2/ α, (where µ_1, µ_2 and µ_3 are constants) and α = sqrt (a_{ij} y^i y^j) be a Riemannian metric and β be a 1-form. Further, we prove that if α is a positive (negative) sectional curvature and F is of α-parallel Ricci curvature with constant Killing 1-form β, then (M, F) is a Riemannian Einstein space