Motivated by the study of CR-submanifolds of codimension $2$ in ${ℂ}^4$, the authors consider here a $6$-dimensional oriented manifold $M$ equipped with a $4$-dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on $M$; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures. The local ’flat’ models are a $3$-dimensional complex contact manifold and the product of two $3$-dimensional real contact manifolds, respectively.

EUDML-ID : urn:eudml:doc:220231
Mots clés:

@article{701708,
     title = {Some special geometry in dimension six},
     booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2003},
     pages = {[93]-98},
     mrnumber = {MR1982436},
     zbl = {1047.53018},
     url = {http://dml.mathdoc.fr/item/701708}
}

Čap, Andreas; Eastwood, Michael. Some special geometry in dimension six, dans Proceedings of the 22nd Winter School "Geometry and Physics", GDML_Books,  (2003), pp. [93]-98. http://gdmltest.u-ga.fr/item/701708/