Research Article

First-order invariants of differential 2-forms

Published in: Quaestiones Mathematicae
Volume 45 , issue 7 , 2022 , pages: 1145–1152

DOI: 10.2989/16073606.2021.1929537

Author(s): J. Muñoz Masqué , Spain , L.M. Pozo Coronado , Spain

Keywords: Primary: 53A55 , Secondary: 22E15 , 53D05 , 58A10 , 58A20 , Primary: 53A55 , Secondary: 22E15 , 53D05 , 58A10 , 58A20

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Abstract

Let M be a smooth manifold of dimension 2n, and let OM be the dense open subbundle in ∧² T*M of 2-covectors of maximal rank. The algebra of Diﬀ M -invariant smooth functions of first order on OM is proved to be isomorphic to the algebra of smooth Sp(Ωx)-invariant functions on , x being a fixed point in M , and Ωx a fixed element in (OM )_x. The maximum number of functionally independent invariants is computed.

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