接触多様体とシンプレクティック多様体（第２版） Riemannian Geometry of Contact and Symplectic Manifolds (Progress in Mathematics) 〈Vol. 203〉 （2ND）

Blair, D. E.

Birkhäuser（2010/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 343 p.
• 商品コード 9780817649586

基本説明

The monograph 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.

Full 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. 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.

Contents

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.