Geodesic orbit and weak symmetric spray manifolds

Xiyun Xu; Ming Xu

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arXiv · 2404.03886

Geodesic orbit and weak symmetric spray manifolds

Xiyun Xu·Ming Xu

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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.

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Xiyun Xu, Ming Xu. 2024-04-05. Geodesic orbit and weak symmetric spray manifolds. https://arxiv.org/abs/2404.03886

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