Riemannian Geometry of Contact and Symplectic Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2002
|
| Schriftenreihe: | Progress in Mathematics
203 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds. Principal circle bundles (Chapter 2) are then discussed as a prelude to the Boothby--Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on the general setting of Riemannian metrics associated with both symplectic and contact structures, and Chapter 5 is devoted to integral submanifolds of the contact subbundle. Topics treated in the subsequent chapters include Sasakian manifolds, the important study of the curvature of contact metric manifolds, submanifold theory in both the K"hler and Sasakian settings, tangent sphere bundles, curvature functionals, complex contact manifolds and 3-Sasakian manifolds. The book serves both as a general reference for mathematicians to the basic properties of symplectic and contact manifolds and as an excellent resource for graduate students and researchers in the Riemannian geometric arena. The prerequisite for this text is a basic course in Riemannian geometry |
| Beschreibung: | 1 Online-Ressource (XII, 260 p) |
| ISBN: | 9781475736045 9781475736069 |
| DOI: | 10.1007/978-1-4757-3604-5 |
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| 500 | |a This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds. Principal circle bundles (Chapter 2) are then discussed as a prelude to the Boothby--Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on the general setting of Riemannian metrics associated with both symplectic and contact structures, and Chapter 5 is devoted to integral submanifolds of the contact subbundle. Topics treated in the subsequent chapters include Sasakian manifolds, the important study of the curvature of contact metric manifolds, submanifold theory in both the K"hler and Sasakian settings, tangent sphere bundles, curvature functionals, complex contact manifolds and 3-Sasakian manifolds. The book serves both as a general reference for mathematicians to the basic properties of symplectic and contact manifolds and as an excellent resource for graduate students and researchers in the Riemannian geometric arena. The prerequisite for this text is a basic course in Riemannian geometry | ||
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Datensatz im Suchindex
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| author | Blair, David E. |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-3604-5 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9781475736045 9781475736069 |
| language | English |
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| spelling | Blair, David E. Verfasser aut Riemannian Geometry of Contact and Symplectic Manifolds by David E. Blair Boston, MA Birkhäuser Boston 2002 1 Online-Ressource (XII, 260 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 203 This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds. Principal circle bundles (Chapter 2) are then discussed as a prelude to the Boothby--Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on the general setting of Riemannian metrics associated with both symplectic and contact structures, and Chapter 5 is devoted to integral submanifolds of the contact subbundle. Topics treated in the subsequent chapters include Sasakian manifolds, the important study of the curvature of contact metric manifolds, submanifold theory in both the K"hler and Sasakian settings, tangent sphere bundles, curvature functionals, complex contact manifolds and 3-Sasakian manifolds. The book serves both as a general reference for mathematicians to the basic properties of symplectic and contact manifolds and as an excellent resource for graduate students and researchers in the Riemannian geometric arena. The prerequisite for this text is a basic course in Riemannian geometry Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s Symplektische Mannigfaltigkeit (DE-588)4290704-4 s Kontaktmannigfaltigkeit (DE-588)4669522-9 s 1\p DE-604 https://doi.org/10.1007/978-1-4757-3604-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blair, David E. Riemannian Geometry of Contact and Symplectic Manifolds Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4669522-9 (DE-588)4290704-4 (DE-588)4128462-8 |
| title | Riemannian Geometry of Contact and Symplectic Manifolds |
| title_auth | Riemannian Geometry of Contact and Symplectic Manifolds |
| title_exact_search | Riemannian Geometry of Contact and Symplectic Manifolds |
| title_full | Riemannian Geometry of Contact and Symplectic Manifolds by David E. Blair |
| title_fullStr | Riemannian Geometry of Contact and Symplectic Manifolds by David E. Blair |
| title_full_unstemmed | Riemannian Geometry of Contact and Symplectic Manifolds by David E. Blair |
| title_short | Riemannian Geometry of Contact and Symplectic Manifolds |
| title_sort | riemannian geometry of contact and symplectic manifolds |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Kontaktmannigfaltigkeit (DE-588)4669522-9 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Kontaktmannigfaltigkeit Symplektische Mannigfaltigkeit Riemannsche Geometrie |
| url | https://doi.org/10.1007/978-1-4757-3604-5 |
| work_keys_str_mv | AT blairdavide riemanniangeometryofcontactandsymplecticmanifolds |