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

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

E-mail Address: mbabalic@theory.nipne.ro

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and

Mihai Visinescu

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

E-mail Address: mvisin@theory.nipne.ro

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https://doi.org/10.1142/S0217732315501801Cited by:13 (Source: Crossref)

Abstract

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

Keywords:

PACS: 11.30-j, 11.30.Ly, 04.50.Gh

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