First-order invariants of differential 2-forms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866912142518648832 |
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| author | Masqué, Jaime Muñoz Coronado, Luis Miguel Pozo |
| author_facet | Masqué, Jaime Muñoz Coronado, Luis Miguel Pozo |
| contents | Let $M$ be a smooth manifold of dimension $2n$, and let $O_{M}$ be the dense open subbundle in $\wedge^{2}T^{\ast}M$ of $2$-covectors of maximal rank. The algebra of $\operatorname*{Diff}M$-invariant smooth functions of first order on $O_{M}$ is proved to be isomorphic to the algebra of smooth $Sp(Ω_{x})$-invariant functions on $\wedge^{3}T_{x}^{\ast}M$, $x$ being a fixed point in $M$, and $Ω_{x}$ a fixed element in $(O_{M})_{x}$. The maximum number of functionally independent invariants is computed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1812_07284 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | First-order invariants of differential 2-forms Masqué, Jaime Muñoz Coronado, Luis Miguel Pozo Differential Geometry 53A55, 22E15, 53D05, 58A10, 58A20 Let $M$ be a smooth manifold of dimension $2n$, and let $O_{M}$ be the dense open subbundle in $\wedge^{2}T^{\ast}M$ of $2$-covectors of maximal rank. The algebra of $\operatorname*{Diff}M$-invariant smooth functions of first order on $O_{M}$ is proved to be isomorphic to the algebra of smooth $Sp(Ω_{x})$-invariant functions on $\wedge^{3}T_{x}^{\ast}M$, $x$ being a fixed point in $M$, and $Ω_{x}$ a fixed element in $(O_{M})_{x}$. The maximum number of functionally independent invariants is computed. |
| title | First-order invariants of differential 2-forms |
| topic | Differential Geometry 53A55, 22E15, 53D05, 58A10, 58A20 |
| url | https://arxiv.org/abs/1812.07284 |