Conformal Differential Geometry

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Topological, Differential and Conformal Geometry of Surfaces

Author : Norbert A'Campo
Publisher : Springer Nature
ISBN 13 : 3030890325
Total Pages : 282 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Topological, Differential and Conformal Geometry of Surfaces by : Norbert A'Campo

Download or read book Topological, Differential and Conformal Geometry of Surfaces written by Norbert A'Campo and published by Springer Nature. This book was released on 2021-10-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.

Conformal Differential Geometry and Its Generalizations

Author : Maks A. Akivis
Publisher : John Wiley & Sons
ISBN 13 : 1118030885
Total Pages : 404 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Conformal Differential Geometry and Its Generalizations by : Maks A. Akivis

Download or read book Conformal Differential Geometry and Its Generalizations written by Maks A. Akivis and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry Conformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry. It offers the first unified presentation of the subject, which was established more than a century ago. The text is divided into seven chapters, each containing figures, formulas, and historical and bibliographical notes, while numerous examples elucidate the necessary theory. Clear, focused, and expertly synthesized, Conformal Differential Geometry and Its Generalizations * Develops the theory of hypersurfaces and submanifolds of any dimension of conformal and pseudoconformal spaces. * Investigates conformal and pseudoconformal structures on a manifold of arbitrary dimension, derives their structure equations, and explores their tensor of conformal curvature. * Analyzes the real theory of four-dimensional conformal structures of all possible signatures. * Considers the analytic and differential geometry of Grassmann and almost Grassmann structures. * Draws connections between almost Grassmann structures and web theory. Conformal differential geometry, a part of classical differential geometry, was founded at the turn of the century and gave rise to the study of conformal and almost Grassmann structures in later years. Until now, no book has offered a systematic presentation of the multidimensional conformal differential geometry and the conformal and almost Grassmann structures. After years of intense research at their respective universities and at the Soviet School of Differential Geometry, Maks A. Akivis and Vladislav V. Goldberg have written this well-conceived, expertly executed volume to fill a void in the literature. Dr. Akivis and Dr. Goldberg supply a deep foundation, applications, numerous examples, and recent developments in the field. Many of the findings that fill these pages are published here for the first time, and previously published results are reexamined in a unified context. The geometry and theory of conformal and pseudoconformal spaces of arbitrary dimension, as well as the theory of Grassmann and almost Grassmann structures, are discussed and analyzed in detail. The topics covered not only advance the subject itself, but pose important questions for future investigations. This exhaustive, groundbreaking text combines the classical results and recent developments and findings. This volume is intended for graduate students and researchers of differential geometry. It can be especially useful to those students and researchers who are interested in conformal and Grassmann differential geometry and their applications to theoretical physics.

Conformal Differential Geometry

Author : Helga Baum
Publisher : Springer Science & Business Media
ISBN 13 : 3764399090
Total Pages : 161 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Conformal Differential Geometry by : Helga Baum

Download or read book Conformal Differential Geometry written by Helga Baum and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.

Conformal Differential Geometry and Its Generalizations

Author : Vladislav V. Goldberg
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (756 download)

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Book Synopsis Conformal Differential Geometry and Its Generalizations by : Vladislav V. Goldberg

Download or read book Conformal Differential Geometry and Its Generalizations written by Vladislav V. Goldberg and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Differential Geometry of Varieties with Degenerate Gauss Maps

Author : Maks A. Akivis
Publisher : Springer Science & Business Media
ISBN 13 : 0387215115
Total Pages : 272 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Differential Geometry of Varieties with Degenerate Gauss Maps by : Maks A. Akivis

Download or read book Differential Geometry of Varieties with Degenerate Gauss Maps written by Maks A. Akivis and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

Computational Conformal Geometry

Author : Xianfeng David Gu
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computational Conformal Geometry by : Xianfeng David Gu

Download or read book Computational Conformal Geometry written by Xianfeng David Gu and published by . This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Symmetry Breaking Operators for Differential Forms on Spheres

Author : Toshiyuki Kobayashi
Publisher : Springer
ISBN 13 : 9811026572
Total Pages : 192 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Conformal Symmetry Breaking Operators for Differential Forms on Spheres by : Toshiyuki Kobayashi

Download or read book Conformal Symmetry Breaking Operators for Differential Forms on Spheres written by Toshiyuki Kobayashi and published by Springer. This book was released on 2016-10-11 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics.

Families of Conformally Covariant Differential Operators, Q-Curvature and Holography

Author : Andreas Juhl
Publisher : Springer Science & Business Media
ISBN 13 : 3764399007
Total Pages : 490 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Families of Conformally Covariant Differential Operators, Q-Curvature and Holography by : Andreas Juhl

Download or read book Families of Conformally Covariant Differential Operators, Q-Curvature and Holography written by Andreas Juhl and published by Springer Science & Business Media. This book was released on 2009-07-26 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies structural properties of Q-curvature from an extrinsic point of view by regarding it as a derived quantity of certain conformally covariant families of differential operators which are associated to hypersurfaces.

Conformal Geometry and Quasiregular Mappings

Author : Matti Vuorinen
Publisher : Springer
ISBN 13 : 3540392076
Total Pages : 228 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Conformal Geometry and Quasiregular Mappings by : Matti Vuorinen

Download or read book Conformal Geometry and Quasiregular Mappings written by Matti Vuorinen and published by Springer. This book was released on 2006-11-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook and of a research monograph: it is the first introduction to the subject available in English, contains nearly a hundred exercises, a survey of the subject as well as an extensive bibliography and, finally, a list of open problems.

Conformal Geometry of Surfaces in S4 and Quaternions

Author : Francis E. Burstall
Publisher : Springer Science & Business Media
ISBN 13 : 9783540430087
Total Pages : 104 pages
Book Rating : 4.4/5 (3 download)

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Book Synopsis Conformal Geometry of Surfaces in S4 and Quaternions by : Francis E. Burstall

Download or read book Conformal Geometry of Surfaces in S4 and Quaternions written by Francis E. Burstall and published by Springer Science & Business Media. This book was released on 2002-03-05 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Differential Geometry

Author : Erwin Kreyszig
Publisher : Courier Corporation
ISBN 13 : 0486318621
Total Pages : 384 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Differential Geometry by : Erwin Kreyszig

Download or read book Differential Geometry written by Erwin Kreyszig and published by Courier Corporation. This book was released on 2013-04-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Conformal Geometry

Author : Ravi S. Kulkarni
Publisher : Springer-Verlag
ISBN 13 : 3322906167
Total Pages : 245 pages
Book Rating : 4.3/5 (229 download)

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Book Synopsis Conformal Geometry by : Ravi S. Kulkarni

Download or read book Conformal Geometry written by Ravi S. Kulkarni and published by Springer-Verlag. This book was released on 2013-03-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotic Analysis in General Relativity

Author : Thierry Daudé
Publisher : Cambridge University Press
ISBN 13 : 1316649407
Total Pages : 381 pages
Book Rating : 4.3/5 (166 download)

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Book Synopsis Asymptotic Analysis in General Relativity by : Thierry Daudé

Download or read book Asymptotic Analysis in General Relativity written by Thierry Daudé and published by Cambridge University Press. This book was released on 2018-01-11 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to modern methods for classical and quantum fields in general relativity / Thierry Daudé, Dietrich Häfner, and Jean-Philippe Nicolas -- Geometry of black hole spacetimes / Lars Andersson, Thomas B. Ackdahl, and Pieter Blue -- An introduction to Quantum Field Theory on curved space-times / Christian Gerard -- A minicourse on microlocal analysis for wave propagation / Andras Vasy -- An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity / Sean N. Curry and A. Rod Gover

Conformal Maps And Geometry

Author : Dmitry Beliaev
Publisher : World Scientific
ISBN 13 : 178634615X
Total Pages : 240 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Conformal Maps And Geometry by : Dmitry Beliaev

Download or read book Conformal Maps And Geometry written by Dmitry Beliaev and published by World Scientific. This book was released on 2019-11-19 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'I very much enjoyed reading this book … Each chapter comes with well thought-out exercises, solutions to which are given at the end of the chapter. Conformal Maps and Geometry presents key topics in geometric function theory and the theory of univalent functions, and also prepares the reader to progress to study the SLE. It succeeds admirably on both counts.'MathSciNetGeometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm-Loewner evolution.Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.It offers a unique view of the field, as it is one of the first to discuss general theory of univalent maps at a graduate level, while introducing more complex theories of conformal invariants and extremal lengths. Conformal Maps and Geometry is an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution.

Transformation Groups in Differential Geometry

Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 3642619819
Total Pages : 192 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Transformation Groups in Differential Geometry by : Shoshichi Kobayashi

Download or read book Transformation Groups in Differential Geometry written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.

Discrete Differential Geometry

Author : Alexander I. Bobenko
Publisher : American Mathematical Society
ISBN 13 : 1470474565
Total Pages : 432 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Discrete Differential Geometry by : Alexander I. Bobenko

Download or read book Discrete Differential Geometry written by Alexander I. Bobenko and published by American Mathematical Society. This book was released on 2023-09-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.

Energy of Knots and Conformal Geometry

Author : Jun O'Hara
Publisher : World Scientific
ISBN 13 : 9812383166
Total Pages : 306 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Energy of Knots and Conformal Geometry by : Jun O'Hara

Download or read book Energy of Knots and Conformal Geometry written by Jun O'Hara and published by World Scientific. This book was released on 2003 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problem in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting thorough numerical experiments.