Riemannian geometry of contact and symplectic manifolds / David E. Blair.
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 (Chapt...
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Full Text (via Springer) |
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| Format: | eBook |
| Language: | English |
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Boston :
Birkhauser,
[2002]
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| Series: | Progress in mathematics (Boston, Mass.)
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| Subjects: |
MARC
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| 100 | 1 | |a Blair, David E., |d 1940- |0 http://id.loc.gov/authorities/names/nr90005136 |1 http://isni.org/isni/0000000110842672. | |
| 245 | 1 | 0 | |a Riemannian geometry of contact and symplectic manifolds / |c David E. Blair. |
| 264 | 1 | |a Boston : |b Birkhauser, |c [2002] | |
| 264 | 4 | |c ©2002. | |
| 300 | |a 1 online resource (xii, 260 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent. | ||
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| 490 | 1 | |a Progress in mathematics (Boston, Mass.) | |
| 504 | |a Includes bibliographical references (pages 227-252) and index. | ||
| 505 | 0 | 0 | |g 1. |t Symplectic Manifolds -- |g 2. |t Principal S[superscript 1]-bundles -- |g 3. |t Contact Manifolds -- |g 4. |t Associated Metrics -- |g 5. |t Integral Submanifolds and Contact Transformations -- |g 6. |t Sasakian and Cosymplectic Manifolds -- |g 7. |t Curvature of Contact Metric Manifolds -- |g 8. |t Submanifolds of Kahler and Sasakian Manifolds -- |g 9. |t Tangent Bundles and Tangent Sphere Bundles -- |g 10. |t Curvature Functionals on Spaces of Associated Metrics -- |g 11. |t Negative [xi]-sectional Curvature -- |g 12. |t Complex Contact Manifolds -- |g 13. |t 3-Sasakian Manifolds. |
| 520 | |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. | ||
| 546 | |a English. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Contact manifolds. |0 http://id.loc.gov/authorities/subjects/sh85031507. | |
| 650 | 0 | |a Symplectic manifolds. |0 http://id.loc.gov/authorities/subjects/sh85131553. | |
| 650 | 0 | |a Geometry, Riemannian. |0 http://id.loc.gov/authorities/subjects/sh85054159. | |
| 650 | 7 | |a Contact manifolds. |2 fast |0 (OCoLC)fst00876504. | |
| 650 | 7 | |a Geometry, Riemannian. |2 fast |0 (OCoLC)fst00940940. | |
| 650 | 7 | |a Symplectic manifolds. |2 fast |0 (OCoLC)fst01140991. | |
| 776 | 0 | 8 | |i Print version: |a Blair, David E., 1940- |t Riemannian geometry of contact and symplectic manifolds |z 0817642617 |w (DLC) 2001052707 |w (OCoLC)48256138. |
| 830 | 0 | |a Progress in mathematics (Boston, Mass.) |0 http://id.loc.gov/authorities/names/n42019868. | |
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