Lectures on Symplectic Geometry

von Ana Cannas Da Silva

268 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.- Kähler Manifolds.- Complex Manifolds.- Kähler Forms.- Compact Kähler 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.

• Reihe: Lecture Notes in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein Differentialrechnung und -gleichungen
• ISBN: 9783540421955
• Sprache: Englisch
• Erscheinungsdatum: 17.07.2001
• Größe: 235 x 155 mm
• Verlag: Springer