Symplectic Geometry : An Introduction based on the Seminar in Bern, 1992

B. Aebischer

ISBN 10: 3034875142 / ISBN 13: 9783034875141

Published by Birkhäuser Basel, Birkhäuser Basel, 2012

About this Item

Druck auf Anfrage Neuware - Printed after ordering - The seminar Symplectic Geometry at the University of Berne in summer 1992 showed that the topic of this book is a very active field, where many different branches of mathematics come tog9ther: differential geometry, topology, partial differential equations, variational calculus, and complex analysis. As usual in such a situation, it may be tedious to collect all the necessary ingredients. The present book is intended to give the nonspecialist a solid introduction to the recent developments in symplectic and contact geometry. Chapter 1 gives a review of the symplectic group Sp(n,R), sympkctic manifolds, and Hamiltonian systems (last but not least to fix the notations). The 1Iaslov index for closed curves as well as arcs in Sp(n, R) is discussed. This index will be used in chapters 5 and 8. Chapter 2 contains a more detailed account of symplectic manifolds start ing with a proof of the Darboux theorem saying that there are no local in variants in symplectic geometry. The most important examples of symplectic manifolds will be introduced: cotangent spaces and Kahler manifolds. Finally we discuss the theory of coadjoint orbits and the Kostant-Souriau theorem, which are concerned with the question of which homogeneous spaces carry a symplectic structure.

Seller Inventory # 9783034875141

Bibliographic Details

• Title: Symplectic Geometry : An Introduction based on the Seminar in Bern, 1992
• Publisher: Birkhäuser Basel, Birkhäuser Basel
• Publication Date: 2012
• Language: English
• ISBN 10: 3034875142
• ISBN 13: 9783034875141
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 203W x 133H x 15D millimeters 203 millimeters width by 133 millimeters height by 15 millimeters depth
• Weight: 296 grams

About this title

Synopsis

The seminar Symplectic Geometry at the University of Berne in summer 1992 showed that the topic of this book is a very active field, where many different branches of mathematics come tog9ther: differential geometry, topology, partial differential equations, variational calculus, and complex analysis. As usual in such a situation, it may be tedious to collect all the necessary ingredients. The present book is intended to give the nonspecialist a solid introduction to the recent developments in symplectic and contact geometry. Chapter 1 gives a review of the symplectic group Sp(n,R), sympkctic manifolds, and Hamiltonian systems (last but not least to fix the notations). The 1\Iaslov index for closed curves as well as arcs in Sp(n, R) is discussed. This index will be used in chapters 5 and 8. Chapter 2 contains a more detailed account of symplectic manifolds start­ ing with a proof of the Darboux theorem saying that there are no local in­ variants in symplectic geometry. The most important examples of symplectic manifolds will be introduced: cotangent spaces and Kahler manifolds. Finally we discuss the theory of coadjoint orbits and the Kostant-Souriau theorem, which are concerned with the question of which homogeneous spaces carry a symplectic structure.