Generalized Killing spinors in dimension 5

Details Generalized Killing spinors in dimension 5 Generalized Killing spinors in dimension 5

2005-08-21

arxiv.org/abs/math/0508375v2

Trans. Amer. Math. Soc. 359 (2007), no. 11, 5319-5343

Mathematics

Differential Geometry

30 pages. v2: corrected the statement and proof of Theorem 14; added a comment on the embedding property in the non-real-analy

Scientific paper

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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