Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 058, 22 pages      arXiv:1101.5587
Contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”

Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S2×S3

Charles P. Boyer
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA

Received January 28, 2011, in final form June 08, 2011; Published online June 15, 2011

I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold S2×S3. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, Yp,q, discovered by physicists by showing that Yp,q and Yp',q' are inequivalent as contact structures if and only if pp'.

Key words: complete integrability; toric contact geometry; equivalent contact structures; orbifold Hirzebruch surface; contact homology; extremal Sasakian structures.

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