New Einstein-Sasaki and Einstein spaces from Kerr-de Sitter
2009; Springer Nature; Volume: 2009; Issue: 07 Linguagem: Inglês
10.1088/1126-6708/2009/07/082
ISSN1127-2236
AutoresMirjam Cvetič, H. Lü, Don N. Page, C.N. Pope,
Tópico(s)Geometric Analysis and Curvature Flows
ResumoIn this paper, which is an elaboration of our results in Phys. Rev. Lett. 95:071101, 2005 (hep-th/0504225), we construct new Einstein-Sasaki spaces Lp,q,r1,...,rn−1 in all odd dimensions D = 2n+1 ⩾ 5. They arise by taking certain BPS limits of the Euclideanised Kerr-de Sitter metrics. This yields local Einstein-Sasaki metrics of cohomogeneity n, with toric U(1)n+1 principal orbits, and n real non-trivial parameters. By studying the structure of the degenerate orbits we show that for appropriate choices of the parameters, characterised by the (n+1) coprime integers (p,q,r1,...,rn−1), the local metrics extend smoothly onto complete and non-singular compact Einstein-Sasaki manifolds Lp,q,r1,...,rn−1. We also construct new complete and non-singular compact Einstein spaces Λp,q,r1,...,rn in D = 2n+1 that are not Sasakian, by choosing parameters appropriately in the Euclideanised Kerr-de Sitter metrics when no BPS limit is taken.
Referência(s)