Two-step homogeneous geodesics in some homogeneous Finsler manifolds

Abstract

A natural extension of a homogeneous geodesic in homogeneous Riemannian spaces G/H, known as a two-step homogeneous geodesic, can be expressed in the form γ(t)=π(exp(tx)exp(ty)), where x and y are elements of the Lie algebra of G. This paper aims to expand this concept to homogeneous Finsler spaces. We provide certain sufficient conditions for (α,β) spaces and decomposable cubic spaces to possess a one-parameter family of invariant Finsler metrics that can be classified as two-step Finsler geodesic orbit spaces. Additionally, we present some illustrative examples of these spaces. © The Indian National Science Academy 2025.