Superintegrability on three-dimensional Riemannian and relativistic spaces of constant curvature.
Quantum deformations and superintegrable motions on spaces with variable curvature.
Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform.
Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations
Contractions of Poisson-Lie groups are introduced by using Lie bialgebra contractions. As an application, contractions of SL(2,R) Poisson-Lie groups leading to (1+1) Poincaré and Heisenberg structures are analysed. It is shown how the method here introduced allows a systematic construction of the Poisson structures associated to non-coboundary Lie bialgebras. Finally, it is sketched how contractions are also implemented after quantization by using the Lie bialgebra approach.
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