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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.04516 |
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| _version_ | 1866910018127790080 |
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| author | Asuke, Taro |
| author_facet | Asuke, Taro |
| contents | We show that projective structures with torsion are described in terms of affine connections in a parallel way as in the torsion-free case which is done by Kobayashi and Nagano. For this, we make use of a bundle of formal frames, which is a generalization of a bundle of frames. We will also describe projective structures in terms of Thomas--Whitehead connections by following Roberts. In particular, we introduce normal projective connections and show the fundamental theorem for Thomas--Whitehead connections regardless the triviality of the torsion. We will study some examples of projective structures of which the torsion is non-trivial while the curvature is trivial. In this article, projective structures are considered to be the same if they have the same geodesics ignoring parameters and the same torsions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04516 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Notes on projective structures with torsion Asuke, Taro Differential Geometry Primary 53B10, Secondary 53B05 We show that projective structures with torsion are described in terms of affine connections in a parallel way as in the torsion-free case which is done by Kobayashi and Nagano. For this, we make use of a bundle of formal frames, which is a generalization of a bundle of frames. We will also describe projective structures in terms of Thomas--Whitehead connections by following Roberts. In particular, we introduce normal projective connections and show the fundamental theorem for Thomas--Whitehead connections regardless the triviality of the torsion. We will study some examples of projective structures of which the torsion is non-trivial while the curvature is trivial. In this article, projective structures are considered to be the same if they have the same geodesics ignoring parameters and the same torsions. |
| title | Notes on projective structures with torsion |
| topic | Differential Geometry Primary 53B10, Secondary 53B05 |
| url | https://arxiv.org/abs/2301.04516 |