# Curvature as an Integrable Deformation

@article{Ballesteros2019CurvatureAA, title={Curvature as an Integrable Deformation}, author={{\'A}ngel Ballesteros and A. Blasco and Francisco J. Herranz}, journal={arXiv: Mathematical Physics}, year={2019}, pages={1-35} }

The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability properties is reviewed. The constant Gaussian curvature of the underlying spaces is introduced as an explicit deformation parameter, thus allowing the construction of new integrable Hamiltonians in a unified geometric setting in which the Euclidean systems are obtained in the vanishing curvature limit. In particular, the… CONTINUE READING

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