Author | Silva, Ana Cannas da. author |
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Title | Lectures on Symplectic Geometry [electronic resource] / by Ana Cannas da Silva |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-540-45330-7 |
Descript | XII, 220 p. online resource |
Symplectic Manifolds -- Symplectic Forms -- Symplectic Form on the Cotangent Bundle -- Symplectomorphisms -- Lagrangian Submanifolds -- Generating Functions -- Recurrence -- Local Forms -- Preparation for the Local Theory -- Moser Theorems -- Darboux-Moser-Weinstein Theory -- Weinstein Tubular Neighborhood Theorem -- Contact Manifolds -- Contact Forms -- Contact Dynamics -- Compatible Almost Complex Structures -- Almost Complex Structures -- Compatible Triples -- Dolbeault Theory -- Kรคhler Manifolds -- Complex Manifolds -- Kรคhler Forms -- Compact Kรคhler Manifolds -- Hamiltonian Mechanics -- Hamiltonian Vector Fields -- Variational Principles -- Legendre Transform -- Moment Maps -- Actions -- Hamiltonian Actions -- Symplectic Reduction -- The Marsden-Weinstein-Meyer Theorem -- Reduction -- Moment Maps Revisited -- Moment Map in Gauge Theory -- Existence and Uniqueness of Moment Maps -- Convexity -- Symplectic Toric Manifolds -- Classification of Symplectic Toric Manifolds -- Delzant Construction -- Duistermaat-Heckman Theorems