Geodesic
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $S^2\times S^3$. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, $Y^{p,q}$, discovered by physicists by showing that $Y^{p,q}$ and $Y^{p',q'}$ are inequivalent as contact structures if and only if $p\neq p'$.
Keywords: complete integrability; toric contact geometry; equivalent contact structures; orbifold Hirzebruch surface; contact homology; extremal Sasakian structures. 
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     title = {Completely {Integrable} {Contact} {Hamiltonian} {Systems} and {Toric} {Contact} {Structures} on $S^2\times S^3$},
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}
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Charles P. Boyer. Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a57/

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