Differential Analysis on Complex Manifolds

Oscar Garcia-Prada, Raymond O. Wells, Jr.

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English

Springer-Verlag New York Inc.
26 August 2004

Mathematics & Sciences; Calculus & mathematical analysis

Series: Graduate Texts in Mathematics

In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge
*-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.

The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of the developments in the field during the decades since the book appeared.

From a review of the 2nd Edition:

“..the new edition ofProfessor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work.”

Nigel Hitchin, Bulletin of the London Mathematical Society

“Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material.”

By: Raymond O. Wells Jr.
Appendix by: Oscar Garcia-Prada
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of hardcover 3rd ed. 2008
Volume: 65
Dimensions: Height: 235mm, Width: 155mm, Spine: 16mm
Weight: 486g
ISBN: 9781441925350
ISBN 10: 144192535X
Series: Graduate Texts in Mathematics
Pages: 299
Publication Date: 26 August 2004
Audience: Professional and scholarly , Professional and scholarly , Undergraduate , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Reviews for Differential Analysis on Complex Manifolds

"From the reviews of the third edition: ""This is the third edition of a well-known book first published in 1973, with a second edition in 1980. ... It is good to see it back 28 years later. ... For someone learning the material for the first time (or for a professor planning a series of lectures), having such a goal in mind often serves as motivation and gives coherence to the material."" (Fernando Q. Gouvea, MathDL, March, 2008) ""The purpose of the text is to present the basics of analysis and geometry on compact complex manifolds and is already one of the standard sources for this material. ... The book has proven to be an excellent introduction to the theory of complex manifolds considered from both the points of view of complex analysis and differential geometry."" (Vasile Oproiu, Zentralblatt MATH, Vol. 1131, 2008)"