Overview

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.

Full Product Details

Author:   B. Aebischer ,  M. Borer ,  M. Kälin ,  C. Leuenberger
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   Softcover reprint of the original 1st ed. 1994
Volume:   124
Dimensions:   Width: 13.30cm , Height: 1.30cm , Length: 20.30cm
Weight:   0.299kg
ISBN:  

9783034875141

ISBN 10:   3034875142
Pages:   244
Publication Date:   05 November 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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