We find conditions which ensure the integrability of the canonical 3-dimensional distribution V spanned by the Reeb vector fields of an almost 3-contact manifold, showing by an explicit counterexample that the normality of the structures does not necessarily imply the integrability of V. Then we focus on those almost 3-contact metric manifolds for which V is integrable and we define an appropriate notion of almost 3-contact metric connection with torsion. The geometry of an almost 3-contact manifold with torsion is then studied and put in relation with the well-known HKT-geometry.

3-structures with torsion

CAPPELLETTI MONTANO, BENIAMINO
2009

Abstract

We find conditions which ensure the integrability of the canonical 3-dimensional distribution V spanned by the Reeb vector fields of an almost 3-contact manifold, showing by an explicit counterexample that the normality of the structures does not necessarily imply the integrability of V. Then we focus on those almost 3-contact metric manifolds for which V is integrable and we define an appropriate notion of almost 3-contact metric connection with torsion. The geometry of an almost 3-contact manifold with torsion is then studied and put in relation with the well-known HKT-geometry.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/19620
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