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

Document Type : Original Article


Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran E-mail:


In a Finsler spaces, we consider a special (α,β)-metric L satisfying L2(α,β) =
c1 α 2 +2c2 αβ+c3β2, 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 geodesic
vectors and investigate the set of all homogeneous geodesics of invariant (α,β)-metric L on
homogeneous spaces and simply connected 4-dimensional real Lie groups admitting invariant
hypercomplex structure.