Recent Developments In Projective Differential Geometry
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Recent Developments In Projective Differential Geometry
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Author : E. B. Stouffer
language : en
Publisher:
Release Date : 1928*
Recent Developments In Projective Differential Geometry written by E. B. Stouffer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1928* with categories.
Projective Differential Geometry Old And New
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Author : V. Ovsienko
language : en
Publisher: Cambridge University Press
Release Date : 2004-12-13
Projective Differential Geometry Old And New written by V. Ovsienko 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 2004-12-13 with Mathematics categories.
Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.
Current Developments In Differential Geometry And Its Related Fields Proceedings Of The 4th International Colloquium On Differential Geometry And Its Related Fields
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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2015-10-22
Current Developments In Differential Geometry And Its Related Fields Proceedings Of The 4th International Colloquium On Differential Geometry And Its Related Fields written by Toshiaki Adachi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.
This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics.
Projective Differential Geometry Of Curves And Ruled Surfaces
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Author : E. J. Wilczynski
language : en
Publisher: Forgotten Books
Release Date : 2015-06-25
Projective Differential Geometry Of Curves And Ruled Surfaces written by E. J. Wilczynski and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-25 with Mathematics categories.
Excerpt from Projective Differential Geometry of Curves and Ruled Surfaces In the geometrical investigations of the last century, one of the most fundamental distinctions has been that between metrical and projective geometry. It is a curious fact that this classification seems to have given rise to another distinction, which is not at all justified by the nature of things. There are certain properties of curves, surfaces, etc., which may be deduced for the most general configurations of their kind, depending only upon the knowledge that certain conditions of continuity are fulfilled in the vicinity of a certain point. These are the so-called infinitesimal properties and are naturally treated by the methods of the differential calculus. The curious fact to which we have referred is that, but for rare exceptions, these infinitesimal properties have been dealt with only from the metrical point of view. Projective geometry, which has made such progress in the course of the century, has apparently disdained to consider the infinitely small parts into which its configurations may be decomposed. It has gained the possibility of making assertions about its configurations as a whole, only by limiting its field to the consideration of algebraic cases, a restriction which is unnecessary in differential geometry. Between the metrical differential geometry of Monge and Gauss, and the algebraic projective geometry of Poncelet and Plücker, there is left, therefore, the field of projective differential geometry whose nature partakes somewhat of both. The theorems of this kind of geometry are concerned with projeciive properties of the infinitesimal elements. As in the ordinary differential geometry, the process of integration may lead to statements concerning properties of the configuration as a whole. But, of course, such integration is possible only in special cases. Even with this limitation, however, which lies in the nature of things, the field of projective differential geometry is so rich that it seems well worth while to cultivate it with greater energy than has been done heretofore. But few investigations belonging to this field exist. The most important contributions are those of Halphen, who has developed an admirable theory of plane and space curves from this point of view. The author has, in the last few years, built up a projective differential geometry of ruled surfaces. In this book we shall confine ourselves to the consideration of these simplest configurations. If time and strength permit, a general theory of surfaces will follow. In presenting the theories of Halphen, I have nevertheless followed my own methods, both for the sake of uniformity and simplicity. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Recent Progress In Differential Geometry And Its Related Fields
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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2012
Recent Progress In Differential Geometry And Its Related Fields written by Toshiaki Adachi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This volume contains the contributions by the main participants of the 2nd International Colloquium on Differential Geometry and its Related Fields (ICDG2010), held in Veliko Tarnovo, Bulgaria to exchange information on current topics in differential geometry, information geometry and applications. These contributions from active specialists in differential geometry provide significant information on research papers which cover geometric structures, concrete Lie group theory and information geometry. This volume is invaluable not only for researchers in this special area but also for those who are interested in interdisciplinary areas in differential geometry, complex analysis, probability theory and mathematical physics. It also serves as a good guide to graduate students in the field of differential geometry.
Cr Submanifolds Of Complex Projective Space
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Author : Mirjana Djoric
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-09
Cr Submanifolds Of Complex Projective Space written by Mirjana Djoric 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 2009-10-09 with Mathematics categories.
Althoughsubmanifoldscomplexmanifoldshasbeenanactive?eldofstudyfor many years, in some sense this area is not su?ciently covered in the current literature. This text deals with the CR submanifolds of complex manifolds, with particular emphasis on CR submanifolds of complex projective space, and it covers the topics which are necessary for learning the basic properties of these manifolds. We are aware that it is impossible to give a complete overview of these submanifolds, but we hope that these notes can serve as an introduction to their study. We present the fundamental de?nitions and results necessary for reaching the frontiers of research in this ?eld. There are many monographs dealing with some current interesting topics in di?erential geometry, but most of these are written as encyclopedias, or research monographs, gathering recent results and giving the readers ample usefulinformationaboutthetopics. Therefore, thesekindsofmonographsare attractive to specialists in di?erential geometry and related ?elds and acce- able to professional di?erential geometers. However, for graduate students who are less advanced in di?erential geometry, these texts might be hard to read without assistance from their instructors. By contrast, the general philosophy of this book is to begin with the elementary facts about complex manifolds and their submanifolds, give some details and proofs, and introduce the reader to the study of CR submanifolds of complex manifolds; especially complex projective space. It includes only a few original results with precise proofs, while the others are cited in the reference list.
Recent Developments In Geometry And Analysis
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Author : Yuxin Dong
language : en
Publisher: International Pressof Boston Incorporated
Release Date : 2012
Recent Developments In Geometry And Analysis written by Yuxin Dong and has been published by International Pressof Boston Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Projective Differential Geometry Old And New
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Author : Valentin Ovsienko
language : en
Publisher:
Release Date : 2005
Projective Differential Geometry Old And New written by Valentin Ovsienko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Projective differential geometry categories.
Projective Differential Geometry Of Curves And Ruled Surfaces
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Author : Ernest Julius Wilczynski
language : en
Publisher:
Release Date : 1961
Projective Differential Geometry Of Curves And Ruled Surfaces written by Ernest Julius Wilczynski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Geometry, Differential categories.