Complete integrability of geodesics in toric Sasaki-Einstein spaces

23rd International Conference on Integrable Systems and Quantum Symmetries

Visinescu, Mihai^1

Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering, P.O.Box M.G.-6, Magurele, Romania^1

关键词: Complete integrability;    Geometrical property;    Integrability;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012051/pdf
DOI  :  10.1088/1742-6596/670/1/012051

来源: IOP

【 摘 要 】

We describe a method for constructing Killing-Yano tensors on toric Sasaki- Einstein manifolds using their geometrical properties. We take advantage of the fact that the metric cones of these spaces are Calabi-Yau manifolds. The complete list of special Killing forms can be extracted making use of the description of the Calabi-Yau manifolds in terms of toric data. This general procedure for toric Sasaki-Einstein manifolds is exemplified in the case of the 5-dimensional spaces Yp,qand T1,1. Finally we discuss the integrability of geodesic motion in these spaces.