Download or read book Projective Differential Geometry Old and New written by V. Ovsienko and published by Cambridge University Press. This book was released on 2004-12-13 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Projective Differential Geometry Old and New written by Valentin Ovsienko and published by . This book was released on 2005 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective differential geometry of curves and ruled surfaces written by Ernest Julius Wilczynski and published by . This book was released on 1906 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective Differential Geometry The New Haven Mathematical Colloquium written by Ernest Julius WILCZYNSKI and published by . This book was released on 1910 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective Differential Geometry of Curves and Surfaces written by Ernest Preston Lane and published by . This book was released on 2013-09 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective Differential Geometry of Curves and Ruled Surfaces written by E. J. Wilczynski and published by Forgotten Books. This book was released on 2015-06-25 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Projective Differential Geometry of Curves and Ruled Surfaces written by E. J. Wilczynski and published by . This book was released on 1905 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Geometry and Projective Differential Geometry written by J. M. Landsberg and published by . This book was released on 1999 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Projective differential geometry of curves and ruled surfaces written by Ernest Julius Wilczynski and published by . This book was released on 1806 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perspectives on Projective Geometry written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
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.
Download or read book Cartan for Beginners written by Thomas A. Ivey and published by American Mathematical Soc.. This book was released on 2016-12-15 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to G-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective.
Download or read book Projective Differential Geometry written by E. J. Wilczynski and published by Chelsea Publishing Company, Incorporated. This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book C Projective Geometry written by David M Calderbank and published by American Mathematical Society. This book was released on 2021-02-10 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
Download or read book Old and New Questions in Physics Cosmology Philosophy and Theoretical Biology written by Alwyn Van der Merwe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simply to say that this is a collection of essays in honor of the late Wolfgang Yourgrau (1908-1979) is to explain, at least for-the obviously many-"insiders," the unusually wide-ranging title of the present volume. In a Foreword to the Proceedings of the First International Colloquium (focusing on logic, physical reality, and history), held at the University of Denver in May of 1966 under their leadership, Wolfgang Y ourgrau and Allen Breck wrote, in an oblique reference to C. P. Snow: "Indeed there are not two or three or four cultures: there is only one culture; our generation has lost its awareness of this . . . . Historians, logicians, physicists-all are banded in one common enterprise, namely in their des ire to weave an enlightened fabric of human knowledge. " Augment, if you will, the foregoing categories of scholars with biologists, philos ophers, cosmologists, and theologians-all of whom, in addition to historians, Wolf gang Yourgrau, by dint of his inextinguishable enthusiasm and charismatic qualities, assembled in Denver for the Second and Third International Colloquia (in 1967 and 1974, respectively)-and a few other besides, and one arrives at a statement of the credo wh ich Y ourgrau not only professed, but consistently exemplified throughout his adult life.
Download or read book Affine Differential Geometry written by Katsumi Nomizu and published by Cambridge University Press. This book was released on 1994-11-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained and systematic account of affine differential geometry from a contemporary viewpoint, not only covering the classical theory, but also introducing the modern developments that have happened over the last decade. In order both to cover as much as possible and to keep the text of a reasonable size, the authors have concentrated on the significant features of the subject and their relationship and application to such areas as Riemannian, Euclidean, Lorentzian and projective differential geometry. In so doing, they also provide a modern introduction to the last. Some of the important geometric surfaces considered are illustrated by computer graphics, making this a physically and mathematically attractive book for all researchers in differential geometry, and for mathematical physicists seeking a quick entry into the subject.
Download or read book Projective Differential Geometry Of Curves And Surfaces written by Ernest Preston Lane and published by Palala Press. This book was released on 2018-03-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
