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Transversal CR Mappings

Transversal CR Mappings PDF Author: André Minor
Publisher:
ISBN: 9781124661544
Category :
Languages : en
Pages : 68

Book Description
This work will concentrate on transversal CR embeddings of one CR manifold into another both of hypersurface type and nondegenerate. In chapter 2, in lower dimensions and when the target is the sphere, it is shown that at most two such embeddings exists up to holomorphic equivalence. Lifting such an embedding to an isometry between Fefferman bundles is discussed in chapter 3. In chapter 4 it is shown that transversal chain preserving embeddings between CR hypersurfaces must preserve CR structure. Finally in chapter 5 we discuss changes of the CR second fundamental form of a CR embedding by composition with automorphisms of the source and target.

Transversal CR Mappings

Transversal CR Mappings PDF Author: André Minor
Publisher:
ISBN: 9781124661544
Category :
Languages : en
Pages : 68

Book Description
This work will concentrate on transversal CR embeddings of one CR manifold into another both of hypersurface type and nondegenerate. In chapter 2, in lower dimensions and when the target is the sphere, it is shown that at most two such embeddings exists up to holomorphic equivalence. Lifting such an embedding to an isometry between Fefferman bundles is discussed in chapter 3. In chapter 4 it is shown that transversal chain preserving embeddings between CR hypersurfaces must preserve CR structure. Finally in chapter 5 we discuss changes of the CR second fundamental form of a CR embedding by composition with automorphisms of the source and target.

Transversal Mappings and Flows

Transversal Mappings and Flows PDF Author: Ralph Abraham
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 184

Book Description


Transversality of CR Mappings Between CR Submanifolds of Complex Spaces

Transversality of CR Mappings Between CR Submanifolds of Complex Spaces PDF Author: Son Ngoc Duong
Publisher:
ISBN: 9781267335265
Category :
Languages : en
Pages : 58

Book Description
We investigate the geometric property of transversality of holomorphic, formal or CR mappings between real-analytic, formal or smooth generic submanifolds of complex spaces of equidimension as well as of different dimensions. In Chapter 3, we shall consider the CR transversality in equidimension case. The main purpose of this chapter is to show that a holomorphic, formal or smooth CR mapping sending a real-analytic, smooth or formal generic submanifold M into such another Mʹ is CR transversal to the target, provided that the source manifold is of finite bracket type and the mapping is of generic full rank. This result and its corollary completely resolve two questions posed by Peter Ebenfelt and Linda Preiss Rothschild in a paper from 2006. We also show that under a very mild assumption on the source manifold, the generic full rank condition imposed on the mapping is also necessary for the CR transversality to hold. This result confirms a conjecture in a paper by Bernhard Lamel and Nordine Mir. In Chapter 4, we consider the transversality of mappings when the target manifold is of higher dimension. We will restrict ourself to the situation in which both manifolds M and Mʹ are hypersurfaces in Cn1 and CN1 respectively, where 1

Real Submanifolds in Complex Space and Their Mappings (PMS-47)

Real Submanifolds in Complex Space and Their Mappings (PMS-47) PDF Author: M. Salah Baouendi
Publisher: Princeton University Press
ISBN: 1400883962
Category : Mathematics
Languages : en
Pages : 418

Book Description
This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic, and analytical geometry. In turn, these latter areas have been enriched over the years by the study of problems in several complex variables addressed here. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, include extensive preliminary material to make the book accessible to nonspecialists. One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds. They present the main results in this area with a novel and self-contained approach. The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. The authors also give a thorough comparison of the various nondegeneracy conditions for manifolds and mappings and present new geometric interpretations of these conditions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary.

Complex Analysis and CR Geometry

Complex Analysis and CR Geometry PDF Author: Giuseppe Zampieri
Publisher: American Mathematical Soc.
ISBN: 0821844423
Category : Mathematics
Languages : en
Pages : 210

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.

CR Embedded Submanifolds of CR Manifolds

CR Embedded Submanifolds of CR Manifolds PDF Author: Sean N. Curry
Publisher: American Mathematical Soc.
ISBN: 1470435446
Category : CR submanifolds
Languages : en
Pages : 81

Book Description
The authors develop a complete local theory for CR embedded submanifolds of CR manifolds in a way which parallels the Ricci calculus for Riemannian submanifold theory. They define a normal tractor bundle in the ambient standard tractor bundle along the submanifold and show that the orthogonal complement of this bundle is not canonically isomorphic to the standard tractor bundle of the submanifold. By determining the subtle relationship between submanifold and ambient CR density bundles the authors are able to invariantly relate these two tractor bundles, and hence to invariantly relate the normal Cartan connections of the submanifold and ambient manifold by a tractor analogue of the Gauss formula. This also leads to CR analogues of the Gauss, Codazzi, and Ricci equations. The tractor Gauss formula includes two basic invariants of a CR embedding which, along with the submanifold and ambient curvatures, capture the jet data of the structure of a CR embedding. These objects therefore form the basic building blocks for the construction of local invariants of the embedding. From this basis the authors develop a broad calculus for the construction of the invariants and invariant differential operators of CR embedded submanifolds. The CR invariant tractor calculus of CR embeddings is developed concretely in terms of the Tanaka-Webster calculus of an arbitrary (suitably adapted) ambient contact form. This enables straightforward and explicit calculation of the pseudohermitian invariants of the embedding which are also CR invariant. These are extremely difficult to find and compute by more naïve methods. The authors conclude by establishing a CR analogue of the classical Bonnet theorem in Riemannian submanifold theory.

Differential Geometry and Analysis on CR Manifolds

Differential Geometry and Analysis on CR Manifolds PDF Author: Sorin Dragomir
Publisher: Springer Science & Business Media
ISBN: 0817644830
Category : Mathematics
Languages : en
Pages : 499

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

An Introduction to CR Structures

An Introduction to CR Structures PDF Author: Howard Jacobowitz
Publisher: American Mathematical Soc.
ISBN: 0821815334
Category : Mathematics
Languages : en
Pages : 249

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.

Understanding Game Theory: Introduction To The Analysis Of Many Agent Systems With Competition And Cooperation (Second Edition)

Understanding Game Theory: Introduction To The Analysis Of Many Agent Systems With Competition And Cooperation (Second Edition) PDF Author: Vasily N Kolokoltsov
Publisher: World Scientific
ISBN: 9811214875
Category : Mathematics
Languages : en
Pages : 411

Book Description
Steadily growing applications of game theory in modern science (including psychology, biology and economics) require sources to provide rapid access in both classical tools and recent developments to readers with diverse backgrounds. This book on game theory, its applications and mathematical methods, is written with this objective in mind.The book gives a concise but wide-ranging introduction to games including older (pre-game theory) party games and more recent topics like elections and evolutionary games and is generously spiced with excursions into philosophy, history, literature and politics. A distinguished feature is the clear separation of the text into two parts: elementary and advanced, which makes the book ideal for study at various levels.Part I displays basic ideas using no more than four arithmetic operations and requiring from the reader only some inclination to logical thinking. It can be used in a university degree course without any (or minimal) prerequisite in mathematics (say, in economics, business, systems biology), as well as for self-study by school teachers, social and natural scientists, businessmen or laymen. Part II is a rapid introduction to the mathematical methods of game theory, suitable for a mathematics degree course of various levels.To stimulate the mathematical and scientific imagination, graphics by a world-renowned mathematician and mathematics imaging artist, A T Fomenko, are used. The carefully selected works of this artist fit remarkably into the many ideas expressed in the book.This new edition has been updated and enlarged. In particular, two new chapters were added on statistical limit of games with many agents and on quantum games, reflecting possibly the two most stunning trends in the game theory of the 21st century.

Complex Analysis

Complex Analysis PDF Author: Peter Ebenfelt
Publisher: Springer Science & Business Media
ISBN: 3034600097
Category : Mathematics
Languages : en
Pages : 353

Book Description
This volume presents the proceedings of a conference on Several Complex Variables, PDE’s, Geometry, and their interactions held in 2008 at the University of Fribourg, Switzerland, in honor of Linda Rothschild.