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In differential geometry, a symplectic manifold is a smooth manifold, M {\displaystyle M} , equipped with a closed nondegenerate differential 2-form, ω {\displaystyle \omega } , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally in abstract formulations…
Examples, Definition & Lagrangian submanifolds
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displaystyle symplectic omega manifold form lagrangian submanifold field vector manifolds geometry closed called smooth hamiltonian structure cotangent submanifolds 1-form liouville
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Symplectic manifold | is a | smooth manifold | 0.90 | text |
| Symplectic manifold | is a | pair | 0.90 | text |
| Symplectic manifold | related to Basic properties | If | 0.60 | section |
| Symplectic manifold | related to Basic properties | Thus | 0.60 | section |
| Symplectic manifold | related to Basic properties | Unlike | 0.60 | section |
| Symplectic manifold | related to Basic properties | Riemannian | 0.60 | section |
| Symplectic manifold | related to Basic properties | By Darboux's | 0.60 | section |
| Symplectic manifold | related to Basic properties | Consequently | 0.60 | section |
| Symplectic manifold | related to Definition | Let | 0.60 | section |
| Symplectic manifold | related to Definition | Here | 0.60 | section |
| Symplectic manifold | related to Definition | That | 0.60 | section |
| Symplectic manifold | related to Definition | The | 0.60 | section |
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