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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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Additional Information

Diego Conti
Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
Address at time of publication: Dipartimento di Matematica e Applicazioni, Università di Milano – Bicocca, Via Cozzi 53, 20125 Milano, Italy
Email: diego.conti@unimib.it

Simon Salamon
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Email: simon.salamon@polito.it

DOI: https://doi.org/10.1090/S0002-9947-07-04307-3
Received by editor(s): September 2, 2005
Published electronically: May 1, 2007
Additional Notes: This research was carried out as part of the programme “Proprietà geometriche delle varietà reali e complesse” (Cofin 2002) funded by the Italian MIUR
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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