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AuthorAudin, Michรจle. author
TitleSymplectic Geometry of Integrable Hamiltonian Systems [electronic resource] / by Michรจle Audin, Ana Cannas da Silva, Eugene Lerman
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8071-8
Descript X, 226 p. online resource

SUMMARY

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) Mathematical Methods in Physics



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