Foliations In Cauchy Riemann Geometry

Author : Elisabetta Barletta,Sorin Dragomir,Krishan L. Duggal
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 42,6 Mb
Release : 2007
Category : Cauchy-Riemann equations
ISBN : 9780821843048

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Foliations in Cauchy-Riemann Geometry by Elisabetta Barletta,Sorin Dragomir,Krishan L. Duggal Pdf

The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of

Author : Sorin Dragomir
Publisher : Unknown
Page : 402 pages
File Size : 44,5 Mb
Release : 2001
Category : Mathematics
ISBN : UOM:39015059992514

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Selected Topics in Cauchy-Riemann Geometry by Sorin Dragomir Pdf

Author : Philippe Tondeur
Publisher : Birkhäuser
Page : 308 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889148

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Geometry of Foliations by Philippe Tondeur Pdf

The topics in this survey volume concern research done on the differential geom etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.

Author : Vladimir Rovenski
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242703

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Foliations on Riemannian Manifolds and Submanifolds by Vladimir Rovenski Pdf

This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.

Author : Sorin Dragomir,Mohammad Hasan Shahid,Falleh R. Al-Solamy
Publisher : Springer
Page : 390 pages
File Size : 40,6 Mb
Release : 2016-05-31
Category : Mathematics
ISBN : 9789811009167

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Geometry of Cauchy-Riemann Submanifolds by Sorin Dragomir,Mohammad Hasan Shahid,Falleh R. Al-Solamy Pdf

This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

Author : Molino
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468486704

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Riemannian Foliations by Molino Pdf

Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of "plaques". 1---------;- - - - - - Viewed laterally [transver 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di L..... -' _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques.

Author : Krishan L. Duggal,Bayram Sahin
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 55,6 Mb
Release : 2011-02-02
Category : Mathematics
ISBN : 9783034602518

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Differential Geometry of Lightlike Submanifolds by Krishan L. Duggal,Bayram Sahin Pdf

This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.

Author : János Pach,Micha Sharir
Publisher : American Mathematical Soc.
Page : 251 pages
File Size : 54,9 Mb
Release : 2009
Category : Algorithms
ISBN : 9780821846919

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Combinatorial Geometry and Its Algorithmic Applications by János Pach,Micha Sharir Pdf

"Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. "Combinatorial Geometry and Its Algorithmic Applications" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography."--BOOK JACKET.

Author : Ernst Binz,Sonja Pods
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 42,8 Mb
Release : 2008
Category : Heisenberg uncertainty principle
ISBN : 9780821844953

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The Geometry of Heisenberg Groups by Ernst Binz,Sonja Pods Pdf

"The three-dimensional Heisenberg group, being a quite simple non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered." "This book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics."--BOOK JACKET.

Author : Sorin Dragomir,Domenico Perrone
Publisher : Elsevier
Page : 529 pages
File Size : 50,8 Mb
Release : 2011-10-04
Category : Science
ISBN : 9780124160323

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Harmonic Vector Fields by Sorin Dragomir,Domenico Perrone Pdf

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any scientist conducting research in the field of harmonic analysis Provides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds Physical Applications of Geometric Methods

Author : Al Boggess
Publisher : Routledge
Page : 305 pages
File Size : 48,8 Mb
Release : 2017-09-20
Category : Mathematics
ISBN : 9781351457576

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CR Manifolds and the Tangential Cauchy Riemann Complex by Al Boggess Pdf

CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form. The second half of the book is devoted to two significant areas of current research. The first area is the holomorphic extension of CR functions. Both the analytic disc approach and the Fourier transform approach to this problem are presented. The second area of research is the integral kernal approach to the solvability of the tangential Cauchy-Riemann Complex. CR Manifolds and the Tangential Cauchy Riemann Complex will interest students and researchers in the field of several complex variable and partial differential equations.

Author : Nassif Ghoussoub,Amir Moradifam
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 49,8 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780821891520

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Functional Inequalities: New Perspectives and New Applications by Nassif Ghoussoub,Amir Moradifam Pdf

"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.

Author : Kevin Costello
Publisher : American Mathematical Society
Page : 251 pages
File Size : 48,6 Mb
Release : 2022-04-25
Category : Mathematics
ISBN : 9781470470081

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Renormalization and Effective Field Theory by Kevin Costello Pdf

This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantum field theory can learn the powerful methodology of mathematical structure, while mathematicians can position themselves to use the magical ideas of quantum field theory in “mathematics” itself. The retelling of the tale mathematically by Kevin Costello is a beautiful tour de force. —Dennis Sullivan This book is quite a remarkable contribution. It should make perturbative quantum field theory accessible to mathematicians. There is a lot of insight in the way the author uses the renormalization group and effective field theory to analyze perturbative renormalization; this may serve as a springboard to a wider use of those topics, hopefully to an eventual nonperturbative understanding. —Edward Witten Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This book provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin–Vilkovisky formalism. As an example, a cohomological proof of perturbative renormalizability of Yang–Mills theory is presented. An effort has been made to make the book accessible to mathematicians who have had no prior exposure to quantum field theory. Graduate students who have taken classes in basic functional analysis and homological algebra should be able to read this book.

Author : Bennett Chow
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 40,7 Mb
Release : 2007
Category : Global differential geometry
ISBN : 9780821844298

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The Ricci Flow: Techniques and Applications by Bennett Chow Pdf

Author : Warwick De Launey,Dane Laurence Flannery
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 41,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821844960

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Algebraic Design Theory by Warwick De Launey,Dane Laurence Flannery Pdf

Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.