| Título: | Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities. |
| Autores: | Fernández, Marisa ; Stefan, Ivanov ; Muñoz, Vicente ; Ugarte, Luis |
| Tipo de documento: | texto impreso |
| Editorial: | Oxford University Press, 2008 |
| Dimensiones: | application/pdf |
| Nota general: |
info:eu-repo/semantics/restrictedAccess info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometría , Tipo = Artículo |
| Resumen: |
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, ?] when N5 is compact, thus providing a link between the Calabi–Yau structure on the cone N5 × [0, ?] and the nearly K¨ahler structure on the sin-cone N5 × [0, ?]. 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, ?], and the nearly parallel G2-structures on N5 × R2 and (N5 × [0, ?]) × [0, ?]. |
| En línea: | https://eprints.ucm.es/id/eprint/21031/1/VMu%C3%B1oz29.pdf |
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