RT Journal Article
T1 Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities.
A1 Fernández, Marisa
A1 Stefan, Ivanov
A1 Muñoz, Vicente
A1 Ugarte, Luis
AB 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 linkbetween 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 asthe 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 forN5 = 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].
PB Oxford University Press
SN 0024-6107
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/50588
UL https://hdl.handle.net/20.500.14352/50588
LA eng
NO B. S. Acharya, F. Denef, C. Hofman and N. Lambert, ‘Freund–Rubin revisited’, Preprint, 2003,arXiv:hep-th/0308046.H. Baum, T. Friedrich, R. Grunewald and I. Kath, Twistors and Killing spinors on Riemannian manifolds, Seminarbericht Nr. 108 (Humboldt-Universit¨at zu Berlin, 1990).A. Bilal and S. Metzger, ‘Compact weak G2-manifolds with conical singularities’, Nuclear Phys. B 663 (2003) 343–364.D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics 203,(Birkh¨auser,Boston, MA, 2002).C. Boyer and K. Galicki, ‘3-Sasakian manifolds’, Surv. Differential Geom. 6 (1999) 123–184.C. Boyer and K. Galicki, ‘New Einstein metrics in dimension five’, J. Differential Geom. 57 (2001)443–463.C. Boyer, K. Galicki and M. Nakamae, ‘On the geometry of Sasakian–Einstein 5-manifolds’, Math.Ann. 325 (2003) 485–524.R. L. Bryant, ‘Submanifolds and special structures on the octonians’, J. Differential Geom. 17 (1982)185–232.9. R. Bryant and S. Salamon, ‘On the construction of some complete metrics with exceptional holonomy’,Duke Math. J. 58 (1989) 829–850.F. M. Cabrera, ‘SU(3)-structures on hypersurfaces of manifolds with G2-structure’, Monatsh. Math. 148 (2006) 29–50.E. Calabi, ‘Construction and properties of some 6-dimensional almost complex manifolds’, Trans. Amer.Math. Soc. 87 (1958) 407–438.D. Conti and S. Salamon, ‘Generalized Killing spinors in dimension 5’, Trans. Amer. Math. Soc. 359 (2007) 5319–5343.M. Fernandez and A. Gray, ‘Riemannian manifolds with structure group G2’, Ann. Mat. Pura Appl. 32 (1982) 19–45.T. Friedrich and S. Ivanov, ‘Parallel spinors and connections with skew-symmetric torsion in string theory’, Asian J. Math. 6 (2002) 303–335.J. Gauntlett, D. Martelli, J. Sparks and D.Waldram, ‘Sasaki–Einstein metrics on S2 × S3’, Adv.Theor. Math. Phys. 8 (2004) 711–734.A. Gray, ‘Some examples of almost Hermitian manifolds’, Illinois J. Math. 10 (1969) 353–366.A. Gray, ‘Nearly Kahler manifolds’, J. Differential Geom. 4 (1970) 283–309.A. Gray, ‘Riemannian manifolds with geodesic symmetries of order 3’, J. Differential Geom. 7 (1972)343–369.A. Gray, ‘The structure of nearly K¨ahler manifolds’, Math. Ann. 223 (1976) 233–248.N. Hitchin, ‘Stable forms and special metrics’, Global differential geometry: the mathematical legacy of Alfred Gray, Bilbao, 2000, Contemporary Mathematics 288 (American Mathematical Society, Providence,RI, 2001) 70–89.V. Kirichenko, ‘K-spaces of maximal rank’, Mat. Zam. 22 (1977) 465–476 (Russian).D. Martelli and J. Sparks, ‘Toric geometry, Sasaki–Einstein manifolds and a new infinite class of AdS/CFT duals’,Commun. Math. Phys. 262 (2006) 51–89.S. Stock, ‘Lifting SU(3)-structures to nearly parallel G2-structures’, Preprint, 2007, arXiv:0707.2029v1.
NO MCyT
DS Docta Complutense
RD 4 may 2024