Noncompact ${\mathbf{CP}}^N$ as a phase space of superintegrable systems

Abstract

We propose the description of superintegrable models with dynamical $so(1.2)$ symmetry, and of the generic superintegrable deformations of oscillator and Coulomb systems in terms of higher-dimensional Klein model (the non-compact analog of complex projective space) playing the role of phase space. We present the expressions of the constants of motion of these systems via Killing potentials defining the $su(N.1)$ isometries of the Kähler structure.

arXiv comment11 pages, misprints corrected

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Cited by in corpus (1)

• Kähler geometry for $su(1,N|M)$-superconformal mechanics