Two-step homogeneous geodesics in some homogeneous Finsler manifolds

2021/09/06 by Hosseini, Masoumeh, Moghaddam, Hamid Reza Salimi
#22E60 #53C25 #53C30 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.05915

Abstract

A natural extension of a homogeneous geodesic in homogeneous Riemannian spaces G/H, known as a two-step homogeneous geodesic, can be expressed of 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.

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