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arXiv · 0706.0386

Contact 5-manifolds with SU(2)-structure

Luis C. de Andrés·Marisa Fernández·Anna Fino·Luis Ugarte
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Abstract

We consider 5-manifolds with a contact form arising from a hypo structure, which we call \emph{hypo-contact}. We provide conditions which imply that there exists 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 \emph{hypo-contact} structure. This allows us 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 to new metrics with holonomy $G_2$.

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Luis C. de Andrés, Marisa Fernández, Anna Fino, Luis Ugarte. 2008-06-20. Contact 5-manifolds with SU(2)-structure. https://arxiv.org/abs/0706.0386

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