Differential Analysis on Complex Manifolds / Edition 3

by Raymond O. Wells, Oscar Garcia-Prada, R. O. Wells

Overview

A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. 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. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.

Product Details

ISBN-13:	9780387738918
Publisher:	Springer New York
Publication date:	10/28/2007
Series:	Graduate Texts in Mathematics Series , #65
Edition description:	3rd ed. 2008
Pages:	318
Product dimensions:	6.20(w) x 9.30(h) x 0.80(d)

Table of Contents

* Manifolds and Vector Bundles
• Sheaf Theory
• Differential Geometry
• Elliptic Operator Theory
• Compact Complex Manifolds
• Kodaira’s Projective Embedding Theorem
• Appendix by O. Garcia-Prada
• References
• Subject Index
• Author Index

Editorial Reviews

From the reviews of the third edition:

“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.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014)

"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)

From the Publisher