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}
}