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Fernández, Marisa and Stefan, Ivanov and Muñoz, Vicente and Ugarte, Luis (2008) Nearly hypo structures and compact nearly Kähler 6manifolds with conical singularities. Journal of the London Mathematical Society. Second Series, 78 (3). pp. 580604. ISSN 00246107
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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 6dimensional 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 5manifold defines a nearly K¨ahler structure on the sincone 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 sincone 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 5dimensional Lie algebras with nonzero first Betti number. An extension of the concept of nearly Kahler structure is introduced, which we refer to as nearly halfflat SU(3)structure,and which leads us to generalize the construction of nearly parallel G2structures 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 G2structures 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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