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Symplectic Geometry

An Introduction based on the Seminar in Bern, 1992

  • B. Aebischer
  • M. Borer
  • M. Kälin
  • Ch. Leuenberger
  • H. M. Reimann

Part of the Progress in Mathematics book series (PM, volume 124)

Table of contents

  1. Front Matter
    Pages i-xii
  2. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 1-15
  3. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 17-41
  4. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 43-64
  5. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 65-78
  6. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 79-98
  7. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 99-145
  8. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 147-165
  9. B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann
    Pages 167-218
  10. Back Matter
    Pages 219-244

About this book

Introduction

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.

Keywords

contact geometry differential geometry manifold symplectic geometry topology

Authors and affiliations

  • B. Aebischer
    • 1
  • M. Borer
    • 1
  • M. Kälin
    • 1
  • Ch. Leuenberger
    • 1
  • H. M. Reimann
    • 1
  1. 1.Institute of MathematicsBernSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-7512-7
  • Copyright Information Springer Basel AG 1994
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-7514-1
  • Online ISBN 978-3-0348-7512-7
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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