We study the geometry of hypersurfaces in manifolds with Ricci-flat holonomy group, on which we introduce a G-structure whose intrinsic torsion can be identified with the second fundamental form. The general problem of extending a manifold with such a G-structure so as to invert this construction is open, but results exist in particular cases, which we review. We list the five-dimensional nilmanifolds carrying invariant SU (2)-structures of this type, and present an example of an associated metric with holonomy SU(3).
Reduced holonomy, hypersurfaces and extensions
CONTI D;
2006-01-01
Abstract
We study the geometry of hypersurfaces in manifolds with Ricci-flat holonomy group, on which we introduce a G-structure whose intrinsic torsion can be identified with the second fundamental form. The general problem of extending a manifold with such a G-structure so as to invert this construction is open, but results exist in particular cases, which we review. We list the five-dimensional nilmanifolds carrying invariant SU (2)-structures of this type, and present an example of an associated metric with holonomy SU(3).File in questo prodotto:
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