Conformal Differential Geometry And Its Generalizations
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Conformal Differential Geometry And Its Generalizations
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Author : Maks A. Akivis
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-20
Conformal Differential Geometry And Its Generalizations written by Maks A. Akivis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Mathematics categories.
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 And Its Generalizations
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Author : Vladislav V. Goldberg
language : en
Publisher:
Release Date : 2011
Conformal Differential Geometry And Its Generalizations written by Vladislav V. Goldberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Conformal Symmetry Breaking Operators For Differential Forms On Spheres
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Author : Toshiyuki Kobayashi
language : en
Publisher: Springer
Release Date : 2016-10-11
Conformal Symmetry Breaking Operators For Differential Forms On Spheres written by Toshiyuki Kobayashi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-11 with Mathematics categories.
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.
Conformal Differential Geometry
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Author : Helga Baum
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-28
Conformal Differential Geometry written by Helga Baum 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 2011-01-28 with Mathematics categories.
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.
Introduction To M Bius Differential Geometry
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Author : Udo Hertrich-Jeromin
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-14
Introduction To M Bius Differential Geometry written by Udo Hertrich-Jeromin 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 2003-08-14 with Mathematics categories.
This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.
Families Of Conformally Covariant Differential Operators Q Curvature And Holography
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Author : Andreas Juhl
language : en
Publisher: Birkhäuser
Release Date : 2009-08-29
Families Of Conformally Covariant Differential Operators Q Curvature And Holography written by Andreas Juhl and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Mathematics categories.
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.
Differential Geometry
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Author : R.W. Sharpe
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-11-21
Differential Geometry written by R.W. Sharpe 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 2000-11-21 with Mathematics categories.
Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.
Conformal Geometry Of Surfaces In S4 And Quaternions
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Author : Francis E. Burstall
language : en
Publisher: Springer
Release Date : 2004-10-20
Conformal Geometry Of Surfaces In S4 And Quaternions written by Francis E. Burstall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-20 with Mathematics categories.
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 Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.
Differential Geometry In The Large
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Author : Owen Dearricott
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-22
Differential Geometry In The Large written by Owen Dearricott 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 2020-10-22 with Mathematics categories.
From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher: Springer Nature
Release Date : 2021-10-27
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-27 with Mathematics categories.
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.