Generating Functions, Symplectic Geometry, and Applications

  title={Generating Functions, Symplectic Geometry, and Applications},
  author={Claude Viterbo},
A symplectic form on a manifold is a closed two form UJ, nondegenerate as a skewsymmetric bilinear form on the tangent space at each point. Integration of the form on a two-dimensional submanifold S with boundary 8S in M associates to S a real number (positive or negative) the "area of 5", which due to Stokes' formula only depends on the curves dS, and the homology class of S rei dS. If moreover the form is exact, that is UJ = dX, the area of S is obtained by integrating A over dS. In this case… CONTINUE READING


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1 Excerpt

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