Real And Complex Geometry

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Perspectives On Projective Geometry

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Author : Jürgen Richter-Gebert
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04

Perspectives On Projective Geometry written by Jürgen Richter-Gebert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-04 with Mathematics categories.

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Several Complex Variables And The Geometry Of Real Hypersurfaces

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Author : John P. D'Angelo
language : en
Publisher: Routledge
Release Date : 2019-07-16

Several Complex Variables And The Geometry Of Real Hypersurfaces written by John P. D'Angelo and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-16 with Mathematics categories.

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Fully Nonlinear Pdes In Real And Complex Geometry And Optics

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Author : Luca Capogna
language : en
Publisher: Springer
Release Date : 2013-10-07

Fully Nonlinear Pdes In Real And Complex Geometry And Optics written by Luca Capogna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-07 with Mathematics categories.

The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.

Complex Geometry

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Author : Daniel Huybrechts
language : en
Publisher: Springer Science & Business Media
Release Date : 2005

Complex Geometry written by Daniel Huybrechts and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.

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)

Real And Complex Geometry

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Author : Liviu Ornea
language : en
Publisher: Springer Nature
Release Date : 2025-08-02

Real And Complex Geometry written by Liviu Ornea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-02 with Mathematics categories.

The book covers a wide area of hot subjects in real and complex differential geometry, such as conformal geometry, special holonomy, Sasakian geometry, Kähler and non-Kähler metrics, classification of compact complex surfaces, Einstein metrics, bi-Hermitian geometry, non-integrable almost complex structures, etc. All of these are rather close to Paul Gauduchon’s themes and influential results in the past fifty years. The reader will find fifteen papers – a few surveys, but the majority containing new and exciting results. The book thus gives an idea of the present research interests of some of the best experts today in real and complex differential geometry including Vestislav Apostolov, Florin Belgun, Charles Boyer, Georges Dloussky, Anna Fino, Gueo Grantcharov, Claude LeBrun, Andrei Moroianu, Massimiliano Pontecorvo, Simon Salamon, Andrew Swann, Adriano Tomassini, Valentino Tosatti, and Misha Verbitsky.

Riemann Surfaces By Way Of Complex Analytic Geometry

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Author : Dror Varolin
language : en
Publisher: American Mathematical Soc.
Release Date :

Riemann Surfaces By Way Of Complex Analytic Geometry written by Dror Varolin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

Geometry Of Complex Numbers

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Author : Hans Schwerdtfeger
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23

Geometry Of Complex Numbers written by Hans Schwerdtfeger and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Complex Kleinian Groups

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Author : Angel Cano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-05

Complex Kleinian Groups written by Angel Cano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-05 with Mathematics categories.

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.​

Real Algebraic Varieties

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Author : Frédéric Mangolte
language : en
Publisher: Springer Nature
Release Date : 2020-09-21

Real Algebraic Varieties written by Frédéric Mangolte and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-21 with Mathematics categories.

This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.

Classical Algebraic Geometry

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Author : Igor V. Dolgachev
language : en
Publisher: Cambridge University Press
Release Date : 2012-08-16

Classical Algebraic Geometry written by Igor V. Dolgachev and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-16 with Mathematics categories.

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.