An introduction to symplectic geometry

  • Augustin Banyaga
Part of the Progress in Mathematics book series (PM, volume 117)


A symplectic form on a vector space V is a skew-symmetric bilinear form α: V × V → R such that \( \tilde \alpha :V \to V^ \star \tilde \alpha (x)(y) = \alpha (x,y) \) is an isomorphism. Here V* denotes the dual of V.


Vector Bundle Symplectic Form Symplectic Manifold Symplectic Structure Lagrangian Submanifold 
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© Springer Basel AG 1994

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  • Augustin Banyaga

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