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

Pradeep Kumar; T S Madhu; B R Sharath

doi:10.56424/jts.v13i01.10599

Pradeep Kumar Department of Mathematics, School of Engineering, Presidency University,Itgalpura, Bengaluru-560064, Karnataka, India
T S Madhu Department of Mathematics, Sri Jagadguru Renukacharya College of Science, Arts and Commerce, Anand Rao Circle,Bengaluru-560009, Karnataka, India
B R Sharath Department of Mathematics, Vemana Institute of Technology, Bengaluru-560034, Karnataka, India

DOI: https://doi.org/10.56424/jts.v13i01.10599

Keywords: Finsler space, (α, β)-metrics, Ricci tensor, Einstein space, 1-form, Ricci curvature

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