In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Fin...

In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogeneous geodesics on compact semi-simple Lie group is established. We introduce ...

In this paper we describe the complex Randers metrics as the solutions of Zermelo problem of navigation on Hermitian manifolds. Based on it, we construct such examples of complex Randers metrics and we study some of their geometrical properties.

Let $F$ be a left invariant Randers metric on simply connected nilpotent Lie group $N$, induced by Riemannian ${\hat{\textbf{\textit{a}}}}$ and vector field $X$ which is $I_{\hat{\textbf{\textit{a}}}}(M)$-invariant. If the Ricci flow equation has unique solution then, $(N,F)$ soliton if only semialgebraic soliton.


 If a non-reversible Finsler norm is the sum of reversible and closed 1-form, then one can uniquely recover 1-form up to potential fields from boundary distance data. We also show rigidity result for Randers metrics where induced by Riemannian metric which rigid. Our theorems generalize results some manifolds. provide an application seismology seismic wave propagates in moving medium.

Abstract In this work, we extend the study of Schwarzschi ld–Finsler–Randers (SFR) spacetime previously investigated by a subset present authors (Triantafyllopoulos et al. in Eur Phys J C 80(12):1200, 2020; Kapsabelis 81(11):990, 2021). We will examine dynamical analysis geodesics which provides derivation energy and angular momentum particle moving along geodesic SFR spacetime. This allows us ...

‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...