In this paper, we study homogeneous Einstein Kropina metric. First, we characterize the sufficient and necessary condition for a homogeneous Kropina metric to be Einstein and with vanishing S-curvature.Further, we study the conformal deformation of the metric F(α, β) = K(α, β) + ε(x)β, where K(α, β) = α2/ β and ε(x) depends on the position only. Finally, we prove that the conformal deformation of Kropina metric is single colored.
Keywords and Phrases
Homogeneous Finsler space, Einstein space, Ricci curvature, S-curvature, Berwald space, Single colored.
A.M.S. subject classiﬁcation
53B40, 53C20, 53C60.