Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$

Abstract

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 $Y^{p^{\prime },q^{\prime }}$ are inequivalent as contact structures if and only if $p\ne p^{\prime }$.

based on a talk given at the S4 Conference in honor or Willard Miller, Jr

References in corpus (3)

• Canonical Sasakian Metrics
• Supersymmetric AdS Backgrounds in String and M-theory
• Polyfolds And A General Fredholm Theory