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Symplectic Geometry

  • Neil Chriss
  • Victor Ginzburg
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

There are two essential differences between symplectic and Riemannian geometries. First, the Riemannian geometry is “rigid” in the sense that two Riemannian manifolds chosen at random are most likely to be locally nonisometric. On the contrary, any two symplectic manifolds are locally isometric in the sense that the symplectic 2-form on any symplectic manifold always takes the canonical form of Example 1.1.2 in appropriate local coordinates, due to Darboux’s theorem [GS1].

Keywords

Riemannian Manifold Algebraic Geometry Canonical Form Topological Group Essential Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Financial Mathematics DepartmentUniversity of ChicagoChicagoUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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