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Generalized Killing spinors in dimension 5

Diego Conti·Simon Salamon
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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).

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Diego Conti, Simon Salamon. 2006-06-29. Generalized Killing spinors in dimension 5. https://arxiv.org/abs/math/0508375

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