S-curvature for a new class of (α, β) -metrics

Abstract

In this paper, we will investigate the S-curvature, the Landsberg curvature, mean Landsberg curvature, Cartan torsion and mean Cartan torsion for recently introduced (α, β) -metric F=β+aα2+β2α in Pişcoran and Mishra (Georgian Math. J. (in press) 2016); where α is a Riemannian metric; β is an 1-form and a∈ (0 , 1 ] is a real positive scalar. We find the necessary and sufficient condition under which this class of Finsler metrics is Riemannian or locally Minkowskian. Finally, we prove that the above mentioned metric has bounded Cartan torsion.