Killing Forms on Kerr-NUT-$(A){\rm d}S$ Spaces of Einstein-Sasaki Type

Abstract

In certain scaling limits the higher-dimensional Euclideanized Kerr-NUT-$(A){\rm d}S$ metrics are related to the Einstein-Sasaki ones. The complete set of Killing forms of the Einstein-Sasaki spaces are presented. It is pointed out the existence of two additional Killing forms on these spaces associated with the complex volume form of the Calabi-Yau cone manifold. As a concrete example we present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki $Y(p,q)$ spaces.