KnowraSymplectic geometryLinked fromLinked fromThe 9 pages that link to Symplectic geometry, each with the reason it gives.All 9Related 6Narrower topic 2Compared with 1Hamiltonian mechanicsNarrower topic: Its geometric structure underlies canonical coordinates and Hamiltonian flow.Riemannian geometryCompared with: It emphasizes oriented area and Hamiltonian dynamics rather than lengths and angles.Canonical quantizationRelated: Its structure underlies canonical coordinates and the Poisson brackets used in quantization.Action-angle variablesRelated: Canonical transformations preserve the symplectic structure that action-angle coordinates must retain.Jacobi identityRelated: Poisson brackets arising from symplectic structures satisfy the identity.History of geometryRelated: Its rise shows geometry developing through structures shaped by classical mechanics.Mikhail GromovRelated: Gromov introduced pseudoholomorphic curves as a tool that transformed this field.Vladimir ArnoldRelated: Arnold helped establish this geometry as a central language for classical mechanics.Poincaré–Birkhoff theoremNarrower topic: Area preservation on a surface is the simplest setting for symplectic structure.