Symplectic Geometry: An Introduction based on the Seminar in Bern, 1992: 124 (Progress in Mathematics) - Tapa blanda

Aebischer, B.; Borer, M.; Kälin, M.; Leuenberger, C.; Bach, Hans Martin

 
9783034875141: Symplectic Geometry: An Introduction based on the Seminar in Bern, 1992: 124 (Progress in Mathematics)
Tapa blanda
ISBN 10: 3034875142 ISBN 13: 9783034875141
Editorial: Birkhäuser, 2012

Sinopsis

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.

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Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Birkhäuser
Año de publicación
2012
Idioma
Inglés
ISBN 10 
3034875142
ISBN 13 
9783034875141
Encuadernación
Tapa blanda
Número de páginas
260
Contacto del fabricante
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Darmstadt
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Otras ediciones populares con el mismo título

9783764350642: Symplectic Geometry: An Introduction Based on the Seminar in Bern, 1992: v. 124 (Progress in Mathematics)

Edición Destacada

ISBN 10:  3764350644 ISBN 13:  9783764350642
Editorial: Birkhauser Verlag AG, 1994
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