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| Main Author: | |
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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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Table of 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.