We consider 5-manifolds with a contact form arising from a hypo structure, which we call hypo-contact. We provide existence conditions for such a structure on an oriented hypersurface of a 6-manifold with a half-flat SU(3)-structure. For half-flat manifolds with a Killing vector field X preserving the SU(3)-structure we study the geometry of the orbits space. Moreover, we describe the solvable Lie algebras admitting a hypo-contact structure. This allows us to exhibit examples of Sasakian η-Einstein manifolds, as well as to prove that such structures give rise to new metrics with holonomy SU(3) and G2.
Contact 5-manifolds with SU(2)-structure
FINO, Anna Maria;
2009-01-01
Abstract
We consider 5-manifolds with a contact form arising from a hypo structure, which we call hypo-contact. We provide existence conditions for such a structure on an oriented hypersurface of a 6-manifold with a half-flat SU(3)-structure. For half-flat manifolds with a Killing vector field X preserving the SU(3)-structure we study the geometry of the orbits space. Moreover, we describe the solvable Lie algebras admitting a hypo-contact structure. This allows us to exhibit examples of Sasakian η-Einstein manifolds, as well as to prove that such structures give rise to new metrics with holonomy SU(3) and G2.
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