Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929651183517696 |
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| author | Kimura, Naoki Nakamura, Tomoya |
| author_facet | Kimura, Naoki Nakamura, Tomoya |
| contents | A Koszul-Vinberg manifold is a generalization of a Hessian manifold, and their relation is similar to the relation between Poisson manifolds and symplectic manifolds. Koszul-Vinberg structures and Poisson structures on manifolds extend to the structures on algebroids. A Koszul-Vinberg structure on a left-symmetric algebroid is regarded as a symmetric analogue of a Poisson structure on a Lie algebroid. We define a Jacobi-Koszul-Vinberg structure on a Jacobi-left-symmetric algebroid as a symmetric analogue of a Jacobi structure on a Jacobi algebroid. We show some properties of Jacobi-Koszul-Vinberg structures on Jacobi algebroids and give the definition of a Jacobi-Koszul-Vinberg manifold, which is a symmetric analogue of a Jacobi manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids Kimura, Naoki Nakamura, Tomoya Symplectic Geometry Differential Geometry 53D17, 53B12, 53B05, 17D25 A Koszul-Vinberg manifold is a generalization of a Hessian manifold, and their relation is similar to the relation between Poisson manifolds and symplectic manifolds. Koszul-Vinberg structures and Poisson structures on manifolds extend to the structures on algebroids. A Koszul-Vinberg structure on a left-symmetric algebroid is regarded as a symmetric analogue of a Poisson structure on a Lie algebroid. We define a Jacobi-Koszul-Vinberg structure on a Jacobi-left-symmetric algebroid as a symmetric analogue of a Jacobi structure on a Jacobi algebroid. We show some properties of Jacobi-Koszul-Vinberg structures on Jacobi algebroids and give the definition of a Jacobi-Koszul-Vinberg manifold, which is a symmetric analogue of a Jacobi manifold. |
| title | Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids |
| topic | Symplectic Geometry Differential Geometry 53D17, 53B12, 53B05, 17D25 |
| url | https://arxiv.org/abs/2412.20103 |