Riemannian geometry of contact and symplectic manifolds. 2nd ed. (English) Zbl 1246.53001

Blair, David E.

Progress in Mathematics 203. Boston, MA: Birkhäuser (ISBN 978-0-8176-4958-6/hbk; 978-0-8176-4959-3/ebook). xvi, 343 p. (2010).

Publisher’s description: 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.
This 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.

MSC:

53-02	Research exposition (monographs, survey articles) pertaining to differential geometry
53D25	Geodesic flows in symplectic geometry and contact geometry
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
57R17	Symplectic and contact topology in high or arbitrary dimension
53C55	Global differential geometry of Hermitian and Kählerian manifolds
53D35	Global theory of symplectic and contact manifolds
53D05	Symplectic manifolds (general theory)
53D10	Contact manifolds (general theory)

Keywords:

symplectic manifolds; contact manifolds; complex geodesic flow

Citations:

Zbl 1011.53001