A Born Structure on the Tangent Bundle of a Hessian Manifold
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913967538962432 |
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| author | Sakamoto, Hakobi |
| author_facet | Sakamoto, Hakobi |
| contents | The Hessian structure, introduced by Shima(1976), is a geometric structure consisting of a pair $(\nabla,g)$ of an affine connection $\nabla$ and a Riemannian metric $g$ satisfying certain conditions. On the other hand, the Born structure, introduced by Freidel et al.(2014), is a strictly stronger geometric structure than an almost (para-)Hermitian structure. Marotta and Szabo(2019) proved that for a given manifold endowed with a pair $(\nabla, g)$, one can introduce an almost Born structure on the tangent bundle. In this article, we study the equivalence between the conditions that the pair $(\nabla, g)$ defines a Hessian structure, and that the induced almost Born structure is integrable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Born Structure on the Tangent Bundle of a Hessian Manifold Sakamoto, Hakobi Differential Geometry The Hessian structure, introduced by Shima(1976), is a geometric structure consisting of a pair $(\nabla,g)$ of an affine connection $\nabla$ and a Riemannian metric $g$ satisfying certain conditions. On the other hand, the Born structure, introduced by Freidel et al.(2014), is a strictly stronger geometric structure than an almost (para-)Hermitian structure. Marotta and Szabo(2019) proved that for a given manifold endowed with a pair $(\nabla, g)$, one can introduce an almost Born structure on the tangent bundle. In this article, we study the equivalence between the conditions that the pair $(\nabla, g)$ defines a Hessian structure, and that the induced almost Born structure is integrable. |
| title | A Born Structure on the Tangent Bundle of a Hessian Manifold |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.23264 |