The topology of 3-dimensional Hessian manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912910982250496 |
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| author | Gnandi, Emmanuel |
| author_facet | Gnandi, Emmanuel |
| contents | We investigate the global topology of 3-dimensional Hessian manifolds. We prove that any compact, orientable 3-dimensional Hessian manifold is either a Hantzsche-Wendt manifold or admits the structure of a Kähler mapping torus. We analyze the parity of Betti numbers for compact, orientable 3-dimensional Hessian manifolds, with special focus on those of Koszul type (hyperbolic manifolds). Moreover, we show that the product of two compact, orientable, 3-dimensional Hessian manifolds of Koszul type naturally carries a Kähler structure. Finally, we establish that every compact, orientable, 3-dimensional Hessian manifold is a Seifert manifold with trivial Euler number, whose underlying orbifold has either vanishing or negative Euler characteristic, thus providing a complete topological classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The topology of 3-dimensional Hessian manifolds Gnandi, Emmanuel Differential Geometry We investigate the global topology of 3-dimensional Hessian manifolds. We prove that any compact, orientable 3-dimensional Hessian manifold is either a Hantzsche-Wendt manifold or admits the structure of a Kähler mapping torus. We analyze the parity of Betti numbers for compact, orientable 3-dimensional Hessian manifolds, with special focus on those of Koszul type (hyperbolic manifolds). Moreover, we show that the product of two compact, orientable, 3-dimensional Hessian manifolds of Koszul type naturally carries a Kähler structure. Finally, we establish that every compact, orientable, 3-dimensional Hessian manifold is a Seifert manifold with trivial Euler number, whose underlying orbifold has either vanishing or negative Euler characteristic, thus providing a complete topological classification. |
| title | The topology of 3-dimensional Hessian manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.21050 |