An Introduction To Real And Complex Manifolds

Author : R. Narasimhan
Publisher : Elsevier
Page : 263 pages
File Size : 48,8 Mb
Release : 1985-12-01
Category : Mathematics
ISBN : 9780080960227

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Analysis on Real and Complex Manifolds by R. Narasimhan Pdf

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.

Author : Giuliano Sorani
Publisher : Unknown
Page : 226 pages
File Size : 44,9 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39076006354422

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An Introduction to Real and Complex Manifolds by Giuliano Sorani Pdf

Author : R. O. Wells
Publisher : Springer Science & Business Media
Page : 269 pages
File Size : 48,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739466

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Differential Analysis on Complex Manifolds by R. O. Wells Pdf

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 certain developments in the field during the decades since the book first appeared. From reviews of the 2nd Edition: "..the new edition of Professor 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." - Daniel M. Burns, Jr., Mathematical Reviews

Author : Raymond O. Wells
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 51,6 Mb
Release : 2007-10-31
Category : Mathematics
ISBN : 9780387738918

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Differential Analysis on Complex Manifolds by Raymond O. Wells Pdf

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.

Author : Shiing-shen Chern
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 51,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781468493443

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Complex Manifolds without Potential Theory by Shiing-shen Chern Pdf

From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 52,9 Mb
Release : 2005
Category : Computers
ISBN : 3540212906

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Complex Geometry by Daniel Huybrechts Pdf

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Author : James A. Morrow,Kunihiko Kodaira
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 41,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821840559

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Complex Manifolds by James A. Morrow,Kunihiko Kodaira Pdf

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.

Author : Klaus Fritzsche,Hans Grauert
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492736

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From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche,Hans Grauert Pdf

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.

Author : John M. Lee
Publisher : American Mathematical Society
Page : 377 pages
File Size : 47,7 Mb
Release : 2024-05-15
Category : Mathematics
ISBN : 9781470477820

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Introduction to Complex Manifolds by John M. Lee Pdf

Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout. The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.

Author : Steven Bell,J.-L. Brylinski,A.T. Huckleberry,R. Narasimhan,C. Okonek,Georg Schumacher,A. Van de Ven,S. Zucker
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 52,8 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 3540629955

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Complex Manifolds by Steven Bell,J.-L. Brylinski,A.T. Huckleberry,R. Narasimhan,C. Okonek,Georg Schumacher,A. Van de Ven,S. Zucker Pdf

The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.

Author : Raghavan Narasimhan
Publisher : Unknown
Page : 246 pages
File Size : 48,5 Mb
Release : 1973
Category : Electronic
ISBN : 2225392269

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Analysis on Real and Complex Manifolds by Raghavan Narasimhan Pdf

Author : Mike Field
Publisher : Cambridge University Press
Page : 224 pages
File Size : 47,8 Mb
Release : 1982
Category : Complex manifolds
ISBN : 0521288886

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Several Complex Variables and Complex Manifolds by Mike Field Pdf

Annotation This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 51,5 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 1441974008

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 46,8 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387217727

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Introduction to Differentiable Manifolds by Serge Lang Pdf

Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 44,5 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227276

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Introduction to Topological Manifolds by John M. Lee Pdf

Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.