A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions

Abstract

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are Kähler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit expression of local metrics and see how Sasakian structure is deformed by the presence of torsion. We also demonstrate that our example of the metrics admits the existence of hidden symmetries described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an {\it ansatz}, we construct exact solutions in five dimensional minimal (un-)gauged supergravity and eleven dimensional supergravity. Finally, we discuss the global structures of the solutions and obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and $L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven dimensions.

38 pages, 1 table, v2: version to appear in Class. Quant. Grav

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Cited by in corpus (7)

• Black holes, hidden symmetries, and complete integrability
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Generalizations of 3-Sasakian manifolds and skew torsion
• Special Killing forms on toric Sasaki-Einstein manifolds
• The odd side of torsion geometry
• Killing-Yano symmetry of Kaluza-Klein black holes in five dimensions
• Cones of G manifolds and Killing spinors with skew torsion