✦ LIBER ✦

A Darboux theorem for multi-symplectic manifolds

✍ Scribed by Geoffrey Martin

Publisher: Springer
Year: 1988
Tongue: English
Weight: 321 KB
Volume: 16
Category: Article
ISSN: 0377-9017
DOI: 10.1007/bf00402020

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✦ Synopsis

A class of geometric structures defined by i + l-forms that generalize the notion of a symplectlc form is introduced. Examples of these structures occur in multi-dimensional variational calculus. An extension of the Darboux-Moser-Weinstein theorem is proved for these structures and a charactenzataon for their pseudogroups is given.

O. In the/-dimensional calculus of variations the structure of the dynamical equations can be specified by a differential i + 1-form whose domain is the total space of a bundle of/-forms defined over the appropriate jet bundle; see [1] and [4]. Such forms are introduced in a manner analogous to the definition of the canonical 2-form on the cotangent bundle. That is, if A;(N) is the bundle of/-forms over a smooth manifold N, then N ( N ) carries a canonical i-form a o given by O'O

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