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

Abstract

In a Finsler spaces, we consider a special (A, B )-metric L satisfying L^2(A, B ) = c_1A^2 + 2c_2AB + c_3 B^2, where c_i are constant. In this paper, the existence of invariant vector elds on a special homogeneous (A;B )-space with L metric is proved. Then we study geodesic vectors and investigate the set of all homogeneous geodesics of invariant (A;B )-metric L on homogeneous spaces and simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure.