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Progress in Mathematics Ser.: Riemannian Geometry of Contact and Symplectic Manifolds by David E. Blair (2010, Hardcover)
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About this product
Product Identifiers
PublisherBirkhäuser Boston
ISBN-100817649581
ISBN-139780817649586
eBay Product ID (ePID)102860072
Product Key Features
Number of PagesXv, 343 Pages
Publication NameRiemannian Geometry of Contact and Symplectic Manifolds
LanguageEnglish
SubjectGeometry / Non-Euclidean, Geometry / Differential, Topology, Geometry / Algebraic
Publication Year2010
TypeTextbook
Subject AreaMathematics
AuthorDavid E. Blair
SeriesProgress in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight52.9 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
Dewey Edition21
Reviews"The book . . . supplies a lot of examples, and includes many recent results. It 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 submanifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." -Mathematical Reviews"Several examples accompany almost all chapters, in the first book in which the geometry of complex contact manifold[s] is presented. Always, a correct balance between theory and examples is maintained. Also the author gives detail and instructive proofs for basic results and states, without proofs, a great number of interesting results in addition to the corresponding references...[T]his 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." -Memoriile Sectiilor Stiintifice, From the reviews: "The book . . . supplies a lot of examples, and includes many recent results. It 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 submanifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." --Mathematical Reviews "Several examples accompany almost all chapters, in the first book in which the geometry of complex contact manifold[s] is presented. Always, a correct balance between theory and examples is maintained. Also the author gives detail and instructive proofs for basic results and states, without proofs, a great number of interesting results in addition to the corresponding references...[T]his 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." --Memoriile Sectiilor Stiintifice From the reviews of the second edition: "In this book, contact and symplectic manifolds are studied from a Riemannian point of view ... . The book is an excellent reference work for researchers interested in the Riemannian geometry of contact and symplectic manifolds as well as a very good introduction to the subject, containing a lot of examples. The number of examples has even increased compared to the first edition." (Joeri Van der Veken, Mathematical Reviews, Issue 2012 d), From the reviews:"The book . . . supplies a lot of examples, and includes many recent results. It 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 submanifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." -Mathematical Reviews"Several examples accompany almost all chapters, in the first book in which the geometry of complex contact manifold[s] is presented. Always, a correct balance between theory and examples is maintained. Also the author gives detail and instructive proofs for basic results and states, without proofs, a great number of interesting results in addition to the corresponding references...[T]his 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." -Memoriile Sectiilor StiintificeFrom the reviews of the second edition:In this book, contact and symplectic manifolds are studied from a Riemannian point of view … . The book is an excellent reference work for researchers interested in the Riemannian geometry of contact and symplectic manifolds as well as a very good introduction to the subject, containing a lot of examples. The number of examples has even increased compared to the first edition. (Joeri Van der Veken, Mathematical Reviews, Issue 2012 d), From the reviews: "The book . . . supplies a lot of examples, and includes many recent results. It 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 submanifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics." --Mathematical Reviews "Several examples accompany almost all chapters, in the first book in which the geometry of complex contact manifold[s] is presented. Always, a correct balance between theory and examples is maintained. Also the author gives detail and instructive proofs for basic results and states, without proofs, a great number of interesting results in addition to the corresponding references...[T]his 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." --Memoriile Sectiilor Stiintifice From the reviews of the second edition: "In this book, contact and symplectic manifolds are studied from a Riemannian point of view ... . The book is an excellent reference work for researchers interested in the Riemannian geometry of contact and symplectic manifolds as well as a very good introduction to the subject, containing a lot of examples. The number of examples has even increased compared to the first edition." (Joeri Van der Veken, Mathematical Reviews, Issue 2012 d)
Series Volume Number203
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.3/73
Table Of ContentSymplectic 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.
SynopsisThis second edition 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, 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., The author's lectures "Contact Manifolds in Riemannian Geometry", volume 509 (1976), in the Springer-Verlag series Lecture Notes in Mathematics have beenout of print for sometime and it seems approp- ate that an expanded version of this material should become available. Thepresenttext deals withtheRiemannian geometry of bothsymplectic and contact manifolds, although the book is more contact than sympl- tic. This work is based on the recent research of the author, his students, colleagues, andotherscholars, theauthor'sgraduatecoursesat Michigan State University and the earlier lecture notes. Chapter 1 presents the general theory of symplectic manifolds. Pr- cipal circle bundles are then discussed in Chapter 2 as a prelude to the Boothby-Wang ?bration of a compact regular contact manifold in Ch- ter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on Riemannian metrics associated to symplectic and contact structures. Chapter 5 is devoted to integral submanifolds of the contact subbundle. InChapter6wediscussthenormalityofalmostcontactstr- tures, Sasakian manifolds, K-contact manifolds, the relation of contact metricstructures andCR-structures,andcosymplectic structures. Ch- ter 7 deals with the important study of the curvature of a contact metric manifold. In Chapter 8 we give a selection of results on submanifolds of ix x Preface to the First Edition K¨ ahler andSasakian manifolds,includingan illustration of thetechnique of A. Ros in a theorem of F. Urbano on compact minimal Lagrangian n submanifolds in CP .
LC Classification NumberQA641-670
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