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

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)

Citations:

Zbl 1011.53001
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