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Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities.

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Fernández, Marisa and Stefan, Ivanov and Muñoz, Vicente and Ugarte, Luis (2008) Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities. Journal of the London Mathematical Society. Second Series, 78 (3). pp. 580-604. ISSN 0024-6107

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Official URL: http://jlms.oxfordjournals.org/content/78/3/580.full.pdf+html



Abstract

We prove that any totally geodesic hypersurface N5 of a 6-dimensional nearly K¨ahler manifold M6 is a Sasaki–Einstein manifold, and so it has a hypo structure in the sense of Conti and Salamon [Trans. Amer. Math. Soc. 359 (2007) 5319–5343]. We show that any Sasaki–Einstein 5-manifold defines a nearly K¨ahler structure on the sin-cone N5 × R, and a compact nearly Kahler structure with conical singularities on N5 × [0, π] when N5 is compact, thus providing a link
between the Calabi–Yau structure on the cone N5 × [0, π] and the nearly K¨ahler structure on the sin-cone N5 × [0, π]. We define the notion of nearly hypo structure, which leads to a general construction of nearly K¨ahler structure on N5 × R. We characterize double hypo structure as
the intersection of hypo and nearly hypo structures and classify double hypo structures on 5-dimensional Lie algebras with non-zero first Betti number. An extension of the concept of nearly Kahler structure is introduced, which we refer to as nearly half-flat SU(3)-structure,and which leads us to generalize the construction of nearly parallel G2-structures on M6 × R given by Bilal and Metzger [Nuclear Phys. B 663 (2003) 343–364]. For N5 = S5 ⊂ S6 and for
N5 = S2 × S3 ⊂ S3 × S3, we describe explicitly a Sasaki–Einstein hypo structure as well as the corresponding nearly K¨ahler structures on N5 × R and N5 × [0, π], and the nearly parallel G2-structures on N5 × R2 and (N5 × [0, π]) × [0, π].


Item Type:Article
Subjects:Sciences > Mathematics > Geometry
ID Code:21031
Deposited On:24 Apr 2013 13:09
Last Modified:12 Dec 2018 15:13

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