Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1892900 | Journal of Geometry and Physics | 2013 | 6 Pages |
Abstract
We introduce the notion of a manifold admitting a simple compact Cartan 3-form Ï3. We study algebraic types of such manifolds, in particular those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form Ï3. We prove the existence of an algebra of multi-symplectic forms Ïl on these manifolds. Cohomology groups associated with complexes of differential forms on Mn in the presence of such a closed multi-symplectic form Ïl and their relations with the de Rham cohomologies of M are investigated. We show rigidity of a class of strongly associative (resp. strongly coassociative) submanifolds. We include an appendix describing all connected simply connected complete Riemannian manifolds admitting a parallel 3-form.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Hông Vân Lê,