Abstract
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible.
Highlights
Homogeneous spaces are a natural generalization of symmetric spaces and they keep many of their nice properties
The importance of geodesic curves is well known in mathematics and in physics and homogeneous geodesics are, orbits of these symmetries
In Riemannian geometry, homogeneous geodesics were studied by many authors and many results were obtained, see the recent survey paper [1] by the author
Summary
Homogeneous spaces are a natural generalization of symmetric spaces and they keep many of their nice properties. In the papers [3,4], it was proved that this result is optimal, namely, examples of homogeneous Riemannian metrics on solvable Lie groups were constructed which admit just one homogeneous geodesic through any point Generalization of this existence result to pseudo-Riemannian geometry was proved by the author using a different approach in the broader context of homogeneous affine manifolds in [5]. This affine approach was used by the author in [6] to prove that an even-dimensional Lorentzian manifold admits a light-like homogeneous geodesic Generalization of this existence result to Finsler geometry was proved in the series of papers [7] by. Some constructions from [2,10,12] are used
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
