This second edition, divided into fourteen chapters, presents a comprehensivetreatment 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 inChapter 11 for the real case. Both of these topics make use of Étienne Ghys'sattractive 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. New material in most chapters, but particularly in Chapters 3, 7, and 12 Major new topics are covered such as a complex geodesic flow and the accompanying geometry of the projectivized holomorphic tangent bundle Improvements and general corrections based off of the first edition are made throughout Intended for a broad audience of mathematicians, researchers, and students in Riemannian geometry INDICE: Preface .- 1. Symplectic Manifolds .- 2. Principal 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.
- ISBN: 978-0-8176-4958-6
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 344
- Fecha Publicación: 29/08/2010
- Nº Volúmenes: 1
- Idioma: Inglés