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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.03886 |
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| _version_ | 1866909161886842880 |
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| author | Xu, Xiyun Xu, Ming |
| author_facet | Xu, Xiyun Xu, Ming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03886 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geodesic orbit and weak symmetric spray manifolds Xu, Xiyun Xu, Ming Differential Geometry 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. |
| title | Geodesic orbit and weak symmetric spray manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.03886 |