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On the geometry of multisymplectic manifolds

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

F. Cantrijn ,
A. Ibort  and
M. De León
F. Cantrijn
Affiliation:
Theoretical Mechanics Division, University of Gent, Krijgslaan 281, B-9000 Gent, Belgium
A. Ibort
Affiliation:
Departmento de Matematicas, Universidad Carlos III de Madrid, E-28911 Leganes, Madrid, Spain
M. De León
Affiliation:
Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, E-28006 Madrid, Spain
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Abstract

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A multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are considered, and special attention is paid to the canonical multisymplectic structure living on a bundle of exterior k-forms on a manifold. For a class of multisymplectic manifolds admitting a ‘Lagrangian’ fibration, a general structure theorem is given which, in particular, leads to a classification of these manifolds in terms of a prescribed family of cohomology classes.

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 3 , June 1999 , pp. 303 - 330
Copyright
Copyright © Australian Mathematical Society 1999

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