English

Geodesic orbit and weak symmetric spray manifolds

Differential Geometry 2024-04-08 v1

Abstract

In this paper, we introduce the geodesic orbit and weakly symmetric properties in homogeneous spray geometry. When a homogeneous spray manifold is endowed with a reductive decomposition, we can use the spray vector field to describe these properties, and prove that a weakly symmetric spray manifold must be geodesic orbit, which generalizes its analog in homogeneous Riemannian and Finsler geometries.

Keywords

Cite

@article{arxiv.2404.03886,
  title  = {Geodesic orbit and weak symmetric spray manifolds},
  author = {Xiyun Xu and Ming Xu},
  journal= {arXiv preprint arXiv:2404.03886},
  year   = {2024}
}
R2 v1 2026-06-28T15:44:48.839Z