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arXiv · 1505.03976

Complete integrability of geodesic motion in Sasaki-Einstein toric $Y^{p,q}$ spaces

Elena Mirela Babalic·Mihai Visinescu
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Abstract

We construct explicitly the constants of motion for geodesics in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. 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 $Y^{p,q}$ spaces. In the particular case of the homogeneous Sasaki-Einstein manifold $T^{1,1}$ the integrals of motion have simpler forms and the relations between them are described in detail.

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Elena Mirela Babalic, Mihai Visinescu. 2015-05-15. Complete integrability of geodesic motion in Sasaki-Einstein toric $Y^{p,q}$ spaces. https://doi.org/10.1142/s0217732315501801

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