Details
Riemannian Geometry of Contact and Symplectic Manifolds
Progress in Mathematics 2nd ed. 2010
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171,19 € |
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| Verlag: | Birkhäuser |
| Format: | |
| Veröffentl.: | 14.08.2010 |
| ISBN/EAN: | 9780817649593 |
| Sprache: | englisch |
| Anzahl Seiten: | 343 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
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.
<P>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.</P>
<P><EM>Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition</EM> 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.</P>
<P>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.</P>
<P><STRONG>Reviews from the First Edition:</STRONG></P>
<P><EM>"The book . . . can be used either as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the main ideas . . . and studies a vast amount of related subjects such as integral sub-manifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." </EM><STRONG>—Mathematical Reviews</STRONG></P>
<P><EM>"…this is a pleasant and useful book and all geometers will profit [from] reading it. They can use it for advanced courses, for thesis topics as well as for references. Beginners will find in it an attractive [table of] contents and useful ideas for pursuing their studies." </EM><STRONG>—Memoriile Sectiilor Stiintifice</STRONG></P>
<P><EM>Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition</EM> 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.</P>
<P>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.</P>
<P><STRONG>Reviews from the First Edition:</STRONG></P>
<P><EM>"The book . . . can be used either as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the main ideas . . . and studies a vast amount of related subjects such as integral sub-manifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." </EM><STRONG>—Mathematical Reviews</STRONG></P>
<P><EM>"…this is a pleasant and useful book and all geometers will profit [from] reading it. They can use it for advanced courses, for thesis topics as well as for references. Beginners will find in it an attractive [table of] contents and useful ideas for pursuing their studies." </EM><STRONG>—Memoriile Sectiilor Stiintifice</STRONG></P>
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
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