Riemannian Geometry of Contact and Symplectic Manifolds

Erscheinungsjahr 2002
ISBN: 978-0-8176-4261-7
Verlag: Birkhäuser

Buch, Englisch, Band 203, 276 Seiten, Gewicht: 1250 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Blair, David E.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Preface * 1. 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 K"hler
and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles
* 10. Curvature Functionals and Spaces of Associated Metrics * 11.
Negative E-sectional Curvature * 12. Complex Contact Manifolds * 13. 3
-Sasakian Manifolds * Bibliography * Subject Index * Author Index