Differential Analysis on Complex Manifolds

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Beschreibung

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.¿

Zusammenfassung

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. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator. The text moves on to cover harmonic theory on compact manifolds, differential operators on a Kahler manifold, and the Hodge decomposition theorem on compact Kahler manifolds. 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.

Inhaltsverzeichnis

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

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	316
Reihe:	Graduate Texts in Mathematics
Inhalt:	xiii 299 S.
ISBN-13:	9781441925350
ISBN-10:	144192535X
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Wells, Raymond O.
Auflage:	Softcover reprint of hardcover 3rd ed. 2008
Hersteller:	Springer US Springer New York Graduate Texts in Mathematics
Maße:	235 x 155 x 18 mm
Von/Mit:	Raymond O. Wells
Erscheinungsdatum:	23.11.2010
Gewicht:	0,482 kg

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