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| Autori principali: | , , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2412.15771 |
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| _version_ | 1866915073387134976 |
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| author | Masqué, Jaime Muñoz Coronado, Luis Miguel Pozo María, María Eugenia Rosado |
| author_facet | Masqué, Jaime Muñoz Coronado, Luis Miguel Pozo María, María Eugenia Rosado |
| contents | Differential $p$-forms and $q$-vector fields with constant coefficients are studied. Differential $p$-forms of degrees $p=1,2,n-1,n$ with constant coefficients on a smooth $n$-dimensional manifold $M$ are characterized. In the contravariant case, the obstruction for a $q$-vector field $V_q$ to have constant coefficients is proved to be the Schouten-Nijenhuis bracket of $V_q$ with itself. The $q$-vector fields with constant coefficients of degrees $q=1,2,n-1,n$ are also characterized. The notions of differential $p$-forms and $q$-vector fields with conformal constant coefficients are introduced. For arbitrary degrees $p$ and $q$, such differential $p$-forms and $q$-vector fields are seen to be the solutions to two second-order partial differential systems on $J^2(M,\mathbb{R}^n)$, which are reducible to two first-order partial differential systems by adding variables. Computational aspects in solving these systems are discussed and examples and applications are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential $p$-forms and $q$-vector fields with constant coefficients Masqué, Jaime Muñoz Coronado, Luis Miguel Pozo María, María Eugenia Rosado Differential Geometry Primary: 35G20, 35N10, Secondary: 58A10, 58A15, 58A17, 58A20 Differential $p$-forms and $q$-vector fields with constant coefficients are studied. Differential $p$-forms of degrees $p=1,2,n-1,n$ with constant coefficients on a smooth $n$-dimensional manifold $M$ are characterized. In the contravariant case, the obstruction for a $q$-vector field $V_q$ to have constant coefficients is proved to be the Schouten-Nijenhuis bracket of $V_q$ with itself. The $q$-vector fields with constant coefficients of degrees $q=1,2,n-1,n$ are also characterized. The notions of differential $p$-forms and $q$-vector fields with conformal constant coefficients are introduced. For arbitrary degrees $p$ and $q$, such differential $p$-forms and $q$-vector fields are seen to be the solutions to two second-order partial differential systems on $J^2(M,\mathbb{R}^n)$, which are reducible to two first-order partial differential systems by adding variables. Computational aspects in solving these systems are discussed and examples and applications are also given. |
| title | Differential $p$-forms and $q$-vector fields with constant coefficients |
| topic | Differential Geometry Primary: 35G20, 35N10, Secondary: 58A10, 58A15, 58A17, 58A20 |
| url | https://arxiv.org/abs/2412.15771 |