Riemannian Geometry of Contact and Symplectic Manifolds (2nd Ed., 2nd ed. 2010)
5Progress in Mathematics, vol. 203)
Progress in Mathematics Series, Vol. 203

Language: English
Cover of the book Riemannian Geometry of Contact and Symplectic Manifolds

Subject for Riemannian Geometry of Contact and Symplectic Manifolds

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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.

Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition provides new material in most chapters, but a particular emphasis remains on contact manifolds. 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.

Symplectic Manifolds.- Principal S 1-bundles.- Contact Manifolds.- Associated Metrics.- Integral Submanifolds and Contact Transformations.- Sasakian and Cosymplectic Manifolds.- Curvature of Contact Metric Manifolds.- Submanifolds of Kähler and Sasakian Manifolds.- Tangent Bundles and Tangent Sphere Bundles.- Curvature Functionals on Spaces of Associated Metrics.- Negative ?–sectional Curvature.- Complex Contact Manifolds.- Additional Topics in Complex Geometry.- 3-Sasakian Manifolds.- Erratum.
New material in most chapters 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 Includes supplementary material: sn.pub/extras