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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.17212 |
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| _version_ | 1866912315356479488 |
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| author | Tchuiaga, S. Ndiaye, A. Khoule, C. Mohameden, R. A. M. |
| author_facet | Tchuiaga, S. Ndiaye, A. Khoule, C. Mohameden, R. A. M. |
| contents | This paper investigates the transfer of classical geometric structures from a smooth manifold $M$ to its Weil bundle $(M^\mathbf A, \tildeπ_M, M)$ associated with a Weil algebra $\mathbf A$. We show that various structures including locally conformal symplectic (lcs), locally conformal cosymplectic (lcc), contact, Jacobi, Sasakian, Walker, sub Riemannian, orientation, Riemannian, and Kählerian structures admit canonical lifts to $M^\mathbf A$. Our approach emphasizes the differential geometric properties of these canonical constructions, utilizing the Weil projection $\tildeπ_M$ and related functorial tools. This provides a unified perspective on endowing Weil bundles with rich geometric structure inherited from the base manifold. Furthermore, we highlight a specific construction yielding a cosymplectic manifold on $M^\mathbf{A}$ (for suitable $M$ and $\mathbf{A}$) that is demonstrably not a trivial suspension of a symplectic manifold. We also explicitly show how integrability of almost complex structures is preserved and clarify the nature of lifted characteristic vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric structures on Weil bundles: Canonical differential-geometric constructions Tchuiaga, S. Ndiaye, A. Khoule, C. Mohameden, R. A. M. Differential Geometry This paper investigates the transfer of classical geometric structures from a smooth manifold $M$ to its Weil bundle $(M^\mathbf A, \tildeπ_M, M)$ associated with a Weil algebra $\mathbf A$. We show that various structures including locally conformal symplectic (lcs), locally conformal cosymplectic (lcc), contact, Jacobi, Sasakian, Walker, sub Riemannian, orientation, Riemannian, and Kählerian structures admit canonical lifts to $M^\mathbf A$. Our approach emphasizes the differential geometric properties of these canonical constructions, utilizing the Weil projection $\tildeπ_M$ and related functorial tools. This provides a unified perspective on endowing Weil bundles with rich geometric structure inherited from the base manifold. Furthermore, we highlight a specific construction yielding a cosymplectic manifold on $M^\mathbf{A}$ (for suitable $M$ and $\mathbf{A}$) that is demonstrably not a trivial suspension of a symplectic manifold. We also explicitly show how integrability of almost complex structures is preserved and clarify the nature of lifted characteristic vector fields. |
| title | Geometric structures on Weil bundles: Canonical differential-geometric constructions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.17212 |