Mihai Visinescu Complete integrability of geodesic motion in SasakiEinstein toric $Y^{p,q}$ spacesAbstract
We construct explicitly the constants of motion for geodesics in the $5$dimensional
SasakiEinstein spaces $Y^{p,q}$. To carry out this task we use the knowledge of
the complete set of Killing vectors and KillingYano 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 $Y^{p,q}$ spaces. In the particular case of the homogeneous
SasakiEinstein manifold $T^{1,1}$ the integrals of motion have simpler forms and
the relations between them are described in detail.
