Integrability of geodesics and action-angle variables in Sasaki-Einstein space $T^{1,1}$

Abstract

We briefly describe the construction of Stä\-kel-Killing and Killing-Yano tensors on toric Sasaki-Einstein manifolds without working out intricate generalized Killing equations. The integrals of geodesic motions are expressed in terms of Killing vectors and Kill\-ing-Yano tensors of the homogeneous Sasaki-Einstein space $T^{1,1}$. We discuss the integrability of geodesics and construct explicitly the action-angle variables. Two pairs of frequencies of the geodesic motions are resonant giving way to chaotic behavior when the system is perturbed.

13 pages; version to appear in EPJC

References in corpus (3)

• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Chaotic strings in a near Penrose limit of AdS${}_5\times T^{1,1}$
• Complete integrability of geodesic motion in Sasaki-Einstein toric $Y^{p,q}$ spaces

Cited by in corpus (3)

• Action-angle variables for geodesic motions in Sasaki-Einstein spaces $Y^{p,q}$
• Integrability of the geodesic flow on the resolved conifolds over Sasaki-Einstein space $T^{1,1}$
• Generalized action-angle coordinates in toric contact spaces