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arXiv · 1812.07284

First-order invariants of differential 2-forms

Jaime Muñoz Masqué·Luis Miguel Pozo Coronado
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Abstract

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 $Sp(\Omega_{x})$-invariant functions on $\wedge^{3}T_{x}^{\ast}M$, $x$ being a fixed point in $M$, and $\Omega_{x}$ a fixed element in $(O_{M})_{x}$. The maximum number of functionally independent invariants is computed.

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Jaime Muñoz Masqué, Luis Miguel Pozo Coronado. 2018-12-18. First-order invariants of differential 2-forms. https://doi.org/10.2989/16073606.2021.1929537

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