2026/07/06 by Manuel de León, Rubén Izquierdo-López, Manuel Lainz · 1 voice
#math.DG
We study the integrability problem of multisymplectic structures, by identifying them as G-structures. Applying the theory of Spencer cohomology, we give conditions on a multisymplectic form for it to admit a chart in which it has constant coefficients. This general study allows for a rough classification of multisymplectic structures of constant linear type, depending on the natural action of the stabilizer group. The theory is illustrated by providing a scheme for proving a Darboux theorem, which is exemplified with several relevant cases. We also build linear types of multisymplectic forms \varpij whose flatness strictly requires a condition of order j. Finally, the corresponding Lie algebras are computed in the case of field theories.