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Author: Howard Jacobowitz
Publisher: American Mathematical Soc.
ISBN: 0821815334
Category : Mathematics
Languages : en
Pages : 237
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Book Description
The geometry and analysis of CR manifolds is the subject of this expository work, which presents all the basic results on this topic, including results from the ``folklore'' of the subject. The book contains a careful exposition of seminal papers by Cartan and by Chern and Moser, and also includes chapters on the geometry of chains and circles and the existence of nonrealizable CR structures. With its detailed treatment of foundational papers, the book is especially useful in that it gathers in one volume many results that were scattered throughout the literature. Directed at mathematicians and physicists seeking to understand CR structures, this self-contained exposition is also suitable as a text for a graduate course for students interested in several complex variables, differential geometry, or partial differential equations. A particular strength is an extensive chapter that prepares the reader for Cartan's approach to differential geometry. The book assumes only the usual first-year graduate courses as background.
Author: Howard Jacobowitz
Publisher: American Mathematical Soc.
ISBN: 0821815334
Category : Mathematics
Languages : en
Pages : 237
Get Book
Book Description
The geometry and analysis of CR manifolds is the subject of this expository work, which presents all the basic results on this topic, including results from the ``folklore'' of the subject. The book contains a careful exposition of seminal papers by Cartan and by Chern and Moser, and also includes chapters on the geometry of chains and circles and the existence of nonrealizable CR structures. With its detailed treatment of foundational papers, the book is especially useful in that it gathers in one volume many results that were scattered throughout the literature. Directed at mathematicians and physicists seeking to understand CR structures, this self-contained exposition is also suitable as a text for a graduate course for students interested in several complex variables, differential geometry, or partial differential equations. A particular strength is an extensive chapter that prepares the reader for Cartan's approach to differential geometry. The book assumes only the usual first-year graduate courses as background.
Author: Sorin Dragomir
Publisher: Springer Science & Business Media
ISBN: 0817644830
Category : Mathematics
Languages : en
Pages : 499
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Book Description
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study
Author: Robert C. Gunning
Publisher: Princeton University Press
ISBN: 1400889413
Category : Mathematics
Languages : en
Pages : 384
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Book Description
An essential undergraduate textbook on algebra, topology, and calculus An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel. With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning—differentiation, the Riemann integral, series, and differential forms and Stokes's theorem—enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings. Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume. Provides a rigorous introduction to calculus in one and several variables Introduces students to basic topology Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings Discusses differential forms and Stokes's theorem in n dimensions Also covers the Riemann integral, integrability, improper integrals, and series expansions
Author: Marco Abate
Publisher: Springer
ISBN: 3540444874
Category : Mathematics
Languages : en
Pages : 219
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Book Description
The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.
Author: Vicente Cortés
Publisher: European Mathematical Society
ISBN: 9783037190791
Category : Geometry, Riemannian
Languages : en
Pages : 972
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Book Description
The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.
Author: Takao Akahori
Publisher: American Mathematical Soc.
ISBN: 0821824287
Category : Mathematics
Languages : en
Pages : 257
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Book Description
This book is aimed at researchers in complex analysis, several complex variables, or partial differential equations. Kuranishi proved that any abstract strongly pseudo convex CR-structure of real dimension $\geq 9$ can be locally embedded in a complex euclidean space. For the case of real dimension $=3$, there is the famous Nirenberg counter example, but the cases of real dimension $=5$ or 7 were left open. The author of this book establishes the result for real dimension $=7$ and, at the same time, presents a new approach to Kuranishi's result.
Author: G. Komatsu
Publisher: CRC Press
ISBN: 9780824788186
Category : Mathematics
Languages : en
Pages : 250
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Book Description
Presents the proceedings of an international conference on complex geometry and related topics, held in commemoration of the 50th anniversary of Osaka University, Osaka, Japan. The text focuses on the CR invariants, hyperbolic geometry, Yamabe-type problems, and harmonic maps.
Author: William Kingdon Clifford
Publisher: American Mathematical Soc.
ISBN: 0821806076
Category : Science
Languages : en
Pages : 296
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Book Description
This volume is the outgrowth of a conference devoted to William K. Clifford entitled, 'New Trends in Geometrical and Topological Methods', which was held at the University of Madeira in July and August 1995. The aim of the conference was to bring together active workers in fields linked to Clifford's work and to foster the exchange of ideas between mathematicians and theoretical physicists. Divided into 6 one-day sessions, each session was devoted to a specific aspect of Clifford's work. This volume is an attempt to bring the Clifford legacy in a new perspective to a larger community of mathematicians and physicists. New concepts, ideas, and results stemming from Clifford's work are discussed. Each article in the book is a self-contained paper that was presented at or submitted to the conference.
Author: Kristine K. Fowler
Publisher: CRC Press
ISBN: 1482276445
Category : Language Arts & Disciplines
Languages : en
Pages : 475
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Book Description
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathemati
Author: Giuseppe Zampieri
Publisher: American Mathematical Soc.
ISBN: 0821844423
Category : CR submanifolds
Languages : en
Pages : 210
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Book Description
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the $\bar\partial$-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometryrequires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting tograduate students who wish to learn it.
