Inhalt

•  
   Introduction
•  
   Symplectic Group
•  
  Symplectic group
•  
   Marius Souphous Lie
•  
   Emergence of Symplectic Groups
•  
   Weyl and the Symplectic group
•  
   Symplectic Geometry by Siegel
•  
   Carl Ludwig Siegel
•  
   Symplectic geometry by Siegel
•  
   Siegel Modular forms
•  
   Quadratic forms
•  
   Analytical interpretation
•  
   Siegel modular functions of degree n
•  
   Symplectic geometry 1943
•  
   Reception of Siegel's paper 1943
•  
   Siegel's and Hua's parallel works
•  
   Hua Loo-Keng
•  
   Hua in Europe
•  
   Remarks on Siegel's and Hua's parallel work
•  
   Differential forms
•  
   Symplectic form and symplectic space
•  
  Differential forms
•  
   Élie Cartan
•  
   Cartan differential form
•  
   Closed differential forms
•  
   Early applications of differential forms
•  
   Kähler form - Symplectic form
•  
   Erich Kähler
•  
   Kähler Metric
•  
   Reception of Kähler manifolds
•  
   Eckmann and Guggenheimer
•  
   Eckmann and Guggenheimer's work on Kähler manifolds
•  
   Symplectic Manifolds
•  
   Ehresmann and Feldbau
•  
   Jacques Feldbau
•  
   Symplectic Manifolds
•  
   Fibre Spaces, Fibre Bundle
•  
   Almost complexes structures
•  
   Ehresmann: Symplectic Manifolds
•  
   The first reception and the relation between symplectic manifolds and Kähler manifolds
•  
   Siegel's Half Space is a Symplectic Manifold
•  
   Darboux's theorem
•  
  Two versions of Darboux's theorem
•  
   The form used in symplectic geometry
•  
   The classical form
•  
  A look back to the late 19th century
•  
   Pfaffian's Problem
•  
   Gaston Darboux
•  
   The classical theorem of Darboux
•  
  The perspective of symplectic manifolds
•  
   Paulette Libermann
•  
   Equivalence between symplectic structures
•  
   About the name of Darboux's Theorem
•  
   Symplectic Geometry-Lee Hwa-Chung
•  
   About Lee Hwa-Chung Live
•  
   Even dimensional geometry
•  
   Even dimensional manifolds endowed with a nonsingular closed 2-form (Symplectic manifold)
•  
   Conformal flat manifolds
•  
   Automorphisms
•  
   Poisson bracket
•  
   Hamilton's equations
•  
   Equivalence of flat spaces
•  
   Lee Hwa Chung Theorem
•  
   The reception of Lee's work
•  
   Classical Mechanics
•  
  Classical Mechanics
•  
   Lagrangian and Hamiltonian Mechanics
•  
   Symplectic Group and Classical Mechanics
•  
   Aurel Wintner and Canonical Transformations
•  
   Aurel Wintner
•  
   Canonical Transformations
•  
   Lectures on Celestial Mechanics
•  
  Georges Reeb Systémes Dynamiques
•  
   George Reeb
•  
   Systèmes Dynamiques
•  
   Colloque de Géométrie Différentielle
•  
  Basic mathematical concepts
•  
   Lagrangian subspace
•  
   Submanifolds of a Symplectic Manifold
•  
   About the Name: Lagrangian Subspaces
•  
   Symplectomorphisms
•  
   Strasbourg 1953
•  
  Géométrie symplectique différentielle
•  
   Jean-Marie Souriau
•  
   Differential Symplectic Geometry and applications
•  
   Vector Space and Symplectic Vector Space
•  
   Phase space
•  
   Géométrie Symplectique Différentielle
•  
    Les Transformations Canoniques - Sympletomorphisms
•  
   Applications
•  
  Take off
•  
   Symplectic geometry takes off
•  
   Foundations of mechanics
•  
   Symplectic geometry conferences in 1973 and 1974
•  
   Textbooks and journals about symplectic geometry
•  
   Conclusion
•  
   Appendices
•  
   Shiing-Shen Chern
•  
   Chern and Erich Kähler
•  
   Chern and Élie Cartan
•  
   Gauss-Bonnet Theorem
•  
   Vladimir Arnold
•  
   Arnold's conjecture
•  
   Symplectic topology
•  
   Liste of participants
•  
   Geometria simplettica
•  
   Géométrie Symplectique
•  
   Bibliography