In the present work the classical problem of harmonic oscillator in the hyperbolic space H 2 : z 2 0+z 2 1−z 2−z 3 = R has been completely solved in framework of Hamilton–Jacobi equation. We have shown that the harmonic oscillator on H 2 , as in the other spaces with constant curvature, is exactly solvable and belongs to the class of maximally superintegrable system. We have proved that all the...
