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 (12)

• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• Toric Sasaki-Einstein metrics on S^2 x S^3
• Canonical Sasakian Metrics
• A Note on Toric Contact Geometry
• Contact complete integrability
• Contact homology of good toric contact manifolds
• Supersymmetric AdS Backgrounds in String and M-theory
• Polyfolds And A General Fredholm Theory
• The Sasakian Geometry of the Heisenberg Group
• Maximal tori in the symplectomorphism groups of Hirzebruch surfaces
• Extremal Sasakian Metrics on S^3-bundles over S^2

Cited by in corpus (19)

• Contact Hamiltonian Systems
• Infinitesimal symmetries in Contact Hamiltonian systems
• A thermostat algorithm generating target ensembles
• Contact variational integrators
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• Liouville's Theorem and the canonical measure for nonconservative systems from contact geometry
• On the Equivalence Problem for Toric Contact Structures on S^3-bundles over S^2$
• Contact flows and integrable systems
• N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$
• Conformal Gauge Transformations in Thermodynamics
• A review on contact Hamiltonian and Lagrangian systems
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Extremal Sasakian Geometry on $T^2\times S^3$ and Related Manifolds
• Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds
• Contact polarizations and associated metrics in geometric thermodynamics
• Formulation of Stochastic Contact Hamiltonian Systems
• The flow method for the Baker-Campbell-Hausdorff formula: exact results
• Generalized action-angle coordinates in toric contact spaces
• Contact line bundles, foliations, and integrability