Riemannian Geometry of Contact and Symplectic Manifolds
(Sprache: Englisch)
This second edition presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides many illustrative examples for the reader.
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This second edition presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides many illustrative examples for the reader.
Klappentext zu „Riemannian Geometry of Contact and Symplectic Manifolds “
This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides many illustrative examples for the reader. Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. Researchers, mathematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemannian geometry is a prerequisite.
This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view. The monograph examines the basic ideas in detail and provides many illustrative examples for the reader.
Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. New principal topics include a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle and a complex version of the special directions discussed in Chapter 11 for the real case. Both of these topics make use of Étienne Ghys's attractive notion of a holomorphic Anosov flow.
Researchers, mathematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemannian geometry is a prerequisite.
Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. New principal topics include a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle and a complex version of the special directions discussed in Chapter 11 for the real case. Both of these topics make use of Étienne Ghys's attractive notion of a holomorphic Anosov flow.
Researchers, mathematicians, and graduate students in contact and symplectic manifold theory and in Riemannian geometry will benefit from this work. A basic course in Riemannian geometry is a prerequisite.
Inhaltsverzeichnis zu „Riemannian Geometry of Contact and Symplectic Manifolds “
- Preface1. Symplectic Manifolds
2. Principal S1-bundles
3. Contact Manifolds
4. Associated Metrics
5. Integral Submanifolds and Contact Transformations
6. Sasakian and Cosymplectic Manifolds
7. Curvature of Contact Metric Manifolds
8. Submanifolds of Kähler and Sasakian Manifolds
9. Tangent Bundles and Tangent Sphere Bundles
10. Curvature Functionals and Spaces of Associated Metrics
11. Negative Xi-sectional Curvature
12. Complex Contact Manifolds
13. Additional Topics in Complex Geometry
14. 3-Sasakian Manifolds
- Bibliography
- Subject Index
- Author Index
Bibliographische Angaben
- Autor: David E. Blair
- 2010, 2nd ed., 343 Seiten, 6 Schwarz-Weiß-Abbildungen, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0817649581
- ISBN-13: 9780817649586
Sprache:
Englisch
Rezension zu „Riemannian Geometry of Contact and Symplectic Manifolds “
From the reviews:"The book . . . supplies a lot of examples, and includes many recent results. It can be used either as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the main ideas . . . and studies a vast amount of related subjects such as integral submanifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." -Mathematical Reviews
"Several examples accompany almost all chapters, in the first book in which the geometry of complex contact manifold[s] is presented. Always, a correct balance between theory and examples is maintained. Also the author gives detail and instructive proofs for basic results and states, without proofs, a great number of interesting results in addition to the corresponding references...[T]his is a pleasant and useful book and all geometers will profit [from] reading it. They can use it for advanced courses, for thesis topics as well as for references. Beginners will find in it an attractive [table of] contents and useful ideas for pursuing their studies." -Memoriile Sectiilor Stiintifice
From the reviews of the second edition:
"In this book, contact and symplectic manifolds are studied from a Riemannian point of view ... . The book is an excellent reference work for researchers interested in the Riemannian geometry of contact and symplectic manifolds as well as a very good introduction to the subject, containing a lot of examples. The number of examples has even increased compared to the first edition." (Joeri Van der Veken, Mathematical Reviews, Issue 2012 d)
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