Introduction and Motivation

  • Izu Vaisman
Part of the Progress in Mathematics book series (PM)


The aim of this chapter is to motivate the study of symplectic geometry and, particularly, of the transversality of Lagrangian subbundles of a symplectic vector bundle by showing that these subjects are imposed necessarily by partial differential equations and mathematical physics. At the same time, we shall introduce the basic notions of symplectic geometry as they grow out of the study of partial differential equations.


Poisson Bracket Symplectic Manifold Cotangent Bundle Lagrangian Submanifolds Symplectic Geometry 


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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Izu Vaisman
    • 1
  1. 1.Department of MathematicsUniversity of HaifaMount Carmel, HaifaIsrael

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