Complete integrability of geodesic motion in Sasaki-Einstein toric Yp,q spaces

We construct explicitly the constants of motion for geodesics in the five-dimensional Sasaki-Einstein spaces Y-p,Y-q. To carry out this task, we use the knowledge of the complete set of Killing vectors and Killing-Yano tensors on these spaces. In spite of the fact that we generate a multitude of constants of motion, only five of them are functionally independent implying the complete integrability of geodesic flow on Y-p,Y-q spaces. In the particular case of the homogeneous Sasaki-Einstein manifold T-1,T-1 the integrals of motion have simpler forms and the relations between them are described in detail.