Linear F-manifolds, a duality and the generalized tangent bundle
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912515028418560 |
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| author | David, Liana |
| author_facet | David, Liana |
| contents | A linear F-manifold is an F-manifold (E, \circ , e) defined on the total space of a vector bundle π: E \rightarrow M for which the multiplication and unit field are linear tensor fields. We develop a systematic treatment of linear F-manifolds. Using an additional suitable connection on M, we define a duality between linear F-manifolds (with and without Euler fields) on E and the total space E^{*} of the dual vector bundle. Our main examples of linear F-manifolds are the tangent and cotangent prolongation. Motivated by the direct sum of tangent and cotangent prolongation, we define and investigate compatibility conditions between linear F-manifolds and the geometry of the generalized tangent bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear F-manifolds, a duality and the generalized tangent bundle David, Liana Differential Geometry Mathematical Physics A linear F-manifold is an F-manifold (E, \circ , e) defined on the total space of a vector bundle π: E \rightarrow M for which the multiplication and unit field are linear tensor fields. We develop a systematic treatment of linear F-manifolds. Using an additional suitable connection on M, we define a duality between linear F-manifolds (with and without Euler fields) on E and the total space E^{*} of the dual vector bundle. Our main examples of linear F-manifolds are the tangent and cotangent prolongation. Motivated by the direct sum of tangent and cotangent prolongation, we define and investigate compatibility conditions between linear F-manifolds and the geometry of the generalized tangent bundle. |
| title | Linear F-manifolds, a duality and the generalized tangent bundle |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2508.00474 |