From Holomorphic Functions to Complex Manifolds
From Holomorphic Functions to Complex Manifolds

Author: Klaus Fritzsche

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 406

ISBN-13: 146849273X

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This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.

Complex Manifolds
Complex Manifolds

Author: James A. Morrow

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 210

ISBN-13: 082184055X

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Serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, this book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Kahler manifolds called Hodge manifolds is algebraic.

Analysis on Real and Complex Manifolds
Analysis on Real and Complex Manifolds

Author: R. Narasimhan

Publisher: Elsevier

Published: 1985-12-01

Total Pages: 263

ISBN-13: 0080960227

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Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincaré and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem. Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.

Stein Manifolds and Holomorphic Mappings
Stein Manifolds and Holomorphic Mappings

Author: Franc Forstnerič

Publisher: Springer Science & Business Media

Published: 2011-08-27

Total Pages: 501

ISBN-13: 3642222501

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The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.

Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday
Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday

Author: Toshiki Mabuchi

Publisher: World Scientific

Published: 1994-12-09

Total Pages: 261

ISBN-13: 9814501220

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This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein-Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

Hyperbolic Manifolds and Holomorphic Mappings
Hyperbolic Manifolds and Holomorphic Mappings

Author: Shoshichi Kobayashi

Publisher: World Scientific

Published: 2005

Total Pages: 161

ISBN-13: 9812564969

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The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections ?invariant metrics and pseudo-distances? and ?hyperbolic complex manifolds? within the section ?holomorphic mappings?. The invariant distance introduced in the first edition is now called the ?Kobayashi distance?, and the hyperbolicity in the sense of this book is called the ?Kobayashi hyperbolicity? to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.