Killing forms on the five-dimensional Einstein-Sasaki Y(p,q) spaces

Abstract

We present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p,q) spaces. Two new Killing-Yano tensors are identified, associated with the complex volume form of the Calabi-Yau metric cone. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

10 pages; improved version

References in corpus (2)

• Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
• Massless geodesics in $Ad{S}_5\times Y(p,q)$ as a superintegrable system

Cited by in corpus (10)

• Special Killing forms on toric Sasaki-Einstein manifolds
• Complete integrability of geodesic motion in Sasaki-Einstein toric $Y^{p,q}$ spaces
• Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
• Killing-Yano symmetry of Kaluza-Klein black holes in five dimensions
• Sasaki-Ricci flow equation on five-dimensional Sasaki-Einstein space $Y^{p,q}$
• Thermodynamic structure of field equations near apparent horizon for radiating black holes
• Transverse Kähler-Ricci flow and deformations of the metric on the Sasaki space $T^{1,1}$
• Generalized action-angle coordinates in toric contact spaces
• Toric data, Killing forms and complete integrability of geodesics in Sasaki-Einstein spaces $Y^{p,q}$
• Toric data and Killing forms on homogeneous Sasaki-Einstein manifold $T^{1,1}$