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

Authors

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

Keywords and Phrases : : Finsler space, (α, β)-metrics, Ricci tensor, Einstein space, 1-form, Ricci curvature
AMS Subject Classification : : : 53B40, 53C20, 53C60

Submission date : February 17, 2019

Accepted date: May 24, 2019

cited by: J.T.S. Vol. 13 (2019), pp.73-80