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Multisymplectic structures of degree three of product type on 6-dimensional manifolds. (English) Zbl 1052.53036
Slovák, Jan (ed.) et al., The proceedings of the 23th winter school “Geometry and physics”, Srní, Czech Republic, January 18–25, 2003. Palermo: Circolo Matemàtico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 72, 91-98 (2004).
A 3-form on a 6-dimensional manifold $$M$$ is multisymplectic if it satisfies a specific non-degeneracy condition. At each point of $$M$$, such a form gives rise to either a product structure, a complex structure or a tangent structure. In this paper, the author considers multisymplectic 3-forms inducing a product structure at each point and studies their integrability and adapted connections. The other pure cases are studied in other publications [N. Hitchin, J. Differ. Geom. 55, No. 3, 547–576 (2000; Zbl 1036.53042); J. Vanžura, in: Steps in differential geometry, Proceedings of the colloquium on differential geometry, Debrecen, 2000, 375–391 (2001; Zbl 1030.53077)].
For the entire collection see [Zbl 1034.53002].

##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 58A10 Differential forms in global analysis
##### Keywords:
multisymplectic structures; 3-forms; paracomplex structures