A deformation of Sasakian structure in the presence of torsion and supergravity solutions

A deformation of Sasakian structure in the presence of totally skew-symmetric torsion is discussed on odd-dimensional manifolds whose metric cones are Kahler 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 non-trivial odd-rank generalized closed conformal Killing–Yano tensors. Furthermore, using these metrics as an ansatz, we construct exact solutions in five-dimensional minimal gauged/ungauged supergravity and 11-dimensional 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 Sasaki–Einstein manifolds Yp, q and La, b, c. We also briefly discuss regular metrics on non-compact manifolds in 11 dimensions.