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Projective Differential Geometry
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Book Synopsis Projective Differential Geometry Old and New by : V. Ovsienko
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.
Book Synopsis Projective Differential Geometry of Submanifolds by : M.A. Akivis
Download or read book Projective Differential Geometry of Submanifolds written by M.A. Akivis and published by Elsevier. This book was released on 1993-06-30 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations. Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.
Book Synopsis Projective differential geometry of curves and ruled surfaces by : Ernest Julius Wilczynski
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:
Book Synopsis Projective Differential Geometry of Curves and Ruled Surfaces by : E. J. Wilczynski
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.
Book Synopsis Projective Differential Geometry of Curves and Surfaces by : Ernest Preston Lane
Download or read book Projective Differential Geometry of Curves and Surfaces written by Ernest Preston Lane and published by . This book was released on 2012 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Projective Differential Geometry of Curves and Ruled Surfaces by : Ernest Julius Wilczynski
Download or read book Projective Differential Geometry of Curves and Ruled Surfaces written by Ernest Julius Wilczynski and published by Palala Press. This book was released on 2016-05-23 with total page 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.
Book Synopsis C-Projective Geometry by : David M Calderbank
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.
Book Synopsis Lectures in Projective Geometry by : A. Seidenberg
Download or read book Lectures in Projective Geometry written by A. Seidenberg and published by Courier Corporation. This book was released on 2012-06-14 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal text for undergraduate courses, this volume takes an axiomatic approach that covers relations between the basic theorems, conics, coordinate systems and linear transformations, quadric surfaces, and the Jordan canonical form. 1962 edition.
Book Synopsis Symmetries and Overdetermined Systems of Partial Differential Equations by : Michael Eastwood
Download or read book Symmetries and Overdetermined Systems of Partial Differential Equations written by Michael Eastwood and published by Springer Science & Business Media. This book was released on 2009-04-23 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Book Synopsis Projective differential geometry of curves and ruled surfaces by : E J 1876-1932 Wilczynski
Download or read book Projective differential geometry of curves and ruled surfaces written by E J 1876-1932 Wilczynski and published by Legare Street Press. This book was released on 2022-10-27 with total page 0 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 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. 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.
Book Synopsis Projective Differential Geometry of Curves and Ruled Surfaces by : E. J. Wilczynski
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:
Book Synopsis PROJECTIVE DIFFERENTIAL GEOMET by : Ernest Julius 1876-1932 Wilczynski
Download or read book PROJECTIVE DIFFERENTIAL GEOMET written by Ernest Julius 1876-1932 Wilczynski and published by Wentworth Press. This book was released on 2016-08-28 with total page 316 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.
Book Synopsis On the Geometry of Some Special Projective Varieties by : Francesco Russo
Download or read book On the Geometry of Some Special Projective Varieties written by Francesco Russo and published by Springer. This book was released on 2016-01-25 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.
Book Synopsis Algebraic Geometry and Projective Differential Geometry by : J. M. Landsberg
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:
Book Synopsis Projective Differential Geometry Old and New by : Valentin Ovsienko
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:
Book Synopsis Projective Differential Geometry of Triple Systems of Surfaces by : Gabriel Marcus Green
Download or read book Projective Differential Geometry of Triple Systems of Surfaces written by Gabriel Marcus Green and published by . This book was released on 1913 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
