Completeness of superintegrability in two-dimensional
constant-curvature spaces

doi:10.1088/0305-4470/34/22/311

Completeness of superintegrability in two-dimensional constant-curvature spaces

E G Kalnins et al 2001 J. Phys. A: Math. Gen. 34 4705-4720 doi: 10.1088/0305-4470/34/22/311

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E G Kalnins¹, J M Kress¹, G S Pogosyan^2,4 and W Miller Jr³
¹ Department of Mathematics, University of Waikato, Hamilton, New Zealand
² Centro de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Mexico
³ School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
⁴ Permanent address: Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region 14980, Russia.
E-mail: e.kalnins@waikato.ac.nz, jonathan@math.waikato.ac.nz, pogosyan@thsun1.jinr.dubna.su and miller@ima.umn.edu

Abstract. We classify the Hamiltonians H = p_x² + p_y² + V(x,y) of all classical superintegrable systems in two-dimensional complex Euclidean space with two additional second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H = J₁² + J₂² + J₃² + V(x, y, z) on the complex two-sphere where x² + y² + z² = 1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.

PACS numbers: 0230I, 0210D, 0220, 0240, 4520J

Print publication: Issue 22 (8 June 2001)
Received 7 February 2001

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Completeness of superintegrability in two-dimensional constant-curvature spaces

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