A deformation of Sasakian structure in the presence of torsion and supergravity solutions
Abstract
A deformation of Sasakian structure in the presence of totally skewsymmetric torsion is discussed on odddimensional manifolds whose metric cones are Kähler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As their example, we present an explicit expression of local metrics. It is also demonstrated that our example of the metrics admits the existence of hidden symmetry described by nontrivial oddrank generalized closed conformal KillingYano tensors. Furthermore, using these metrics as an ansatz, we construct exact solutions in fivedimensional minimal gauged/ungauged supergravity and 11dimensional supergravity. Finally, the global structures of the solutions are discussed. We obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of SasakiEinstein manifolds Y^{p, q} and L^{a, b, c}. We also briefly discuss regular metrics on noncompact manifolds in 11 dimensions.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 July 2013
 DOI:
 10.1088/02649381/30/13/135008
 arXiv:
 arXiv:1207.0247
 Bibcode:
 2013CQGra..30m5008H
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematics  Differential Geometry
 EPrint:
 38 pages, 1 table, v2: version to appear in Class. Quant. Grav