Homogeneous Finsler spaces with special (α, β)-metric

Finsler geometry is just Riemannian geometry without the quadratic restriction. In Riemannian geometry, the restriction of the metric to a tangent spaceis an inner product and hence tangent spaces at different points are linearlyisometric to each other.In this paper, we consider the special (α, β)-metric such that it is satisfyingF (α, β) = β + aα + βα۲ , a ∈ R. We have investigate the geometric properties of this metric inhomogeneous spaces. We investigate the existence of invariant vector fields. Also, we obtainthe explicit formula for the S-curvature and mean Berwald curvature of homogeneous Finslerspace with this (α, β)-metric. Geodesics and geodesic vectors are other topics that we studyfor these spaces.

کلیدواژه ها:

(&alpha ، ، &beta ، )-metric ، Homogeneous Finsler space ، S-curvature ، Mean Berwald curvature