On the geometry of multisymplectic manifolds

F. Cantrijn, A. Ibort, M. De León
1999 Journal of the Australian Mathematical Society  
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 fc-forms on a manifold. For a class of multisymplectic manifolds admitting a 'Lagrangian' fibration, a
more » ... n' 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. 1991 Mathematics subject classification (Amer. Math. Soc): primary 53C15, 58Axx.
doi:10.1017/s1446788700036636 fatcat:klmpl5eqejf3rpvnwqq73bffqu