Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book)
CONTENT
A Lagrangian Submanifolds -- I Lagrangian and special Lagrangian immersions in Cโ{128}{156} -- II Lagrangian and special Lagrangian submanifolds in symplectic and Calabi-Yau manifolds -- B Symplectic Toric Manifolds -- I Symplectic Viewpoint -- II Algebraic Viewpoint -- C Geodesic Flows and Contact Toric Manifolds -- I From toric integrable geodesic flows to contact toric manifolds -- II Contact group actions and contact moment maps -- III Proof of Theorem I.38 -- List of Contributors
Mathematics
Differential geometry
Manifolds (Mathematics)
Complex manifolds
Physics
Mathematics
Differential Geometry
Manifolds and Cell Complexes (incl. Diff.Topology)
