A Born Structure on the Tangent Bundle of a Hessian Manifold

Fuente: arXiv
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Main Author: Sakamoto, Hakobi
Format: Preprint
Published: 2025
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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