Generalized Killing spinors in dimension 5

Conti, Diego; Salamon, Simon

doi:10.1090/S0002-9947-07-04307-3

Generalized Killing spinors in dimension 5

Authors: Diego Conti and Simon Salamon
Journal: Trans. Amer. Math. Soc. 359 (2007), 5319-5343
MSC (2000): Primary 53C25; Secondary 14J32, 53C29, 53C42, 58A15
DOI: https://doi.org/10.1090/S0002-9947-07-04307-3
Published electronically: May 1, 2007
MathSciNet review: 2327032
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Abstract: We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, $\mathrm{SU}(2)$ -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 $\mathrm{SU}(3)$ .

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