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Yiyan
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Hamiltonian Isotopy class of Lagrangian Submanifold

Let $(X,\omega)$ be a symplectic manifold, $L\subset X$ be a Lagrangian submanifold, $[L]$ denotes the Hamiltonian isotopy class. How to represent $L'\in[L]$ via $L$ (for example, a graph over $L$)? Is there a analogue $\partial\bar{\partial}-$ lemma as in K"{a}hler geometry?

Yiyan
  • 303
  • 1
  • 4