2024/04/05 by Xiyun Xu, Ming Xu, Xu, Xiyun +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2404.03886
openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.