Generalized Killing spinors in dimension 5
Differential Geometry
2007-09-13 v2
Abstract
We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a 5-manifold can be isometrically embedded as a hypersurface in a Calabi-Yau manifold in a natural way. We classify nilmanifolds carrying invariant structures of this type, and present examples of the associated metrics with holonomy SU(3).
Keywords
Cite
@article{arxiv.math/0508375,
title = {Generalized Killing spinors in dimension 5},
author = {Diego Conti and Simon Salamon},
journal= {arXiv preprint arXiv:math/0508375},
year = {2007}
}
Comments
30 pages. v2: corrected the statement and proof of Theorem 14; added a comment on the embedding property in the non-real-analytic case