Hidden symmetries in Sasaki–Einstein geometries

Abstract

We describe a method for constructing Killing–Yano tensors on Sasaki spaces using their geometrical properties, without the need of solving intricate generalized Killing equations. We obtain the Killing–Yano tensors on toric Sasaki–Einstein spaces using the fact that the metric cones of these spaces are Calabi–Yau manifolds which in turn are described in terms of toric data. We extend the search of Killing–Yano tensors on mixed 3-Sasakian manifolds. We illustrate the method by explicit construction of Killing forms on some spaces of current interest.