Invariant vector field on a homogeneous Finsler space with special (α,β)-metric

In a Finsler spaces, we consider a special (α,β)-metric L satisfying L۲(α,β) =c۱ α ۲ +۲c۲ αβ+c۳β۲, where ci are constant. In this paper, the existence of invariant vectorelds on a special homogeneous (α,β)-space with L metric is proved. Then we study geodesicvectors and investigate the set of all homogeneous geodesics of invariant (α,β)-metric L onhomogeneous spaces and simply connected ۴-dimensional real Lie groups admitting invarianthypercomplex structure.

Keywords:

Homogeneous Finsler space , L-metric , invariant vector field , hypercomplex man- ifold , Geodesic vector