Symplectic Geometry: An Introduction based on the Seminar in Bern, 1992
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1994
|
| Schriftenreihe: | Progress in Mathematics
124 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XII, 244 p) |
| ISBN: | 9783034875127 9783034875141 |
| DOI: | 10.1007/978-3-0348-7512-7 |
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| spelling | Aebischer, B. Verfasser aut Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 by B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann Basel Birkhäuser Basel 1994 1 Online-Ressource (XII, 244 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 124 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 Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1992 Bern gnd-content Symplektische Geometrie (DE-588)4194232-2 s 2\p DE-604 Borer, M. Sonstige oth Kälin, M. Sonstige oth Leuenberger, Ch Sonstige oth Reimann, H. M. Sonstige oth https://doi.org/10.1007/978-3-0348-7512-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aebischer, B. Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)1071861417 |
| title | Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 |
| title_auth | Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 |
| title_exact_search | Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 |
| title_full | Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 by B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann |
| title_fullStr | Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 by B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann |
| title_full_unstemmed | Symplectic Geometry An Introduction based on the Seminar in Bern, 1992 by B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger, H. M. Reimann |
| title_short | Symplectic Geometry |
| title_sort | symplectic geometry an introduction based on the seminar in bern 1992 |
| title_sub | An Introduction based on the Seminar in Bern, 1992 |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Symplektische Geometrie Konferenzschrift 1992 Bern |
| url | https://doi.org/10.1007/978-3-0348-7512-7 |
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