Download or read book A Treatise on Projective Differential Geometry A Sequel to the Author s Projective Differential Geometry of Curves and Surfaces written by Ernest Preston LANE and published by . This book was released on 1942 with total page 466 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 Ernest Julius Wilczynski and published by . This book was released on 1906 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1909 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Treatise on the Differential Geometry of Curves and Surfaces by Luther Pfahler Eisenhart, first published in 1909, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
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 Projective Differential Geometry of Curves and Ruled Surfaces written by Ernest Julius Wilczynski and published by . This book was released on 1961 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by Forgotten Books. This book was released on 2015-06-15 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Treatise on the Differential Geometry of Curves and Surfaces This book is a development from courses which I have given in Princeton for a number of years. During this time I have come to feel that more would be accomplished by my students if they had an introductory treatise written in English and otherwise adapted to the use of men beginning their graduate work. Chapter I is devoted to the theory of twisted curves, the method in general being that which is usually followed in discussions of this subject. But in addition I have introduced the idea of moving axes, and have derived the formulas pertaining thereto from the previously obtained Frenet-Serret formulas. In this way the student is made familiar with a method which is similar to that used by Darboux in the first volume of his Leçons, and to that of Cesaro in his Geometria Intrinseca. This method is not only of great advantage in the treatment of certain topics and in the solution of problems, but it is valuable in developing geometrical thinking. The remainder of the book may be divided into three parts. The first, consisting of Chapters II-VI, deals with the geometry of a surface in the neighborhood of a point and the developments therefrom, such as curves and systems of curves defined by differential equations. To a large extent the method is that of Gauss, by which the properties of a surface are derived from the discussion of two quadratic differential forms. However, little or no space is given to the algebraic treatment of differential forms and their invariants. In addition, the method of moving axes, as defined in the first chapter, has been extended so as to be applicable to an investigation of the properties of surfaces and groups of surfaces. The extent of the theory concerning ordinary points is so great that no attempt has been made to consider the exceptional problems. For a discussion of such questions as the existence of integrals of differential equations and boundary conditions the reader must consult the treatises which deal particularly with these subjects. In Chapters VII and VIII the theory previously developed is applied to several groups of surfaces, such as the quadrics, ruled surfaces, minimal surfaces, surfaces of constant total curvature, and surfaces with plane and spherical lines of curvature. 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 A Treatise on Projective Geometry written by Ernest Preston Lane and published by . This book was released on 1942 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by . This book was released on 1960 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Geometry of Curves and Surfaces written by Shoshichi Kobayashi and published by Springer Nature. This book was released on 2019-11-13 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces. Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature K and the mean curvature H —are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain. Then the Gauss–Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number χ(S). Here again, many illustrations are provided to facilitate the reader’s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.
Download or read book A Treatise on the Differential Geometry of Curves and Surfaces written by Luther Pfahler Eisenhart and published by Andesite Press. This book was released on 2017-08-21 with total page 496 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.
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:
Download or read book Image Understanding Workshop written by and published by . This book was released on 1988 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Geometry of Curves and Surfaces written by Victor Andreevich Toponogov and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
Download or read book Differential Geometry of Curves and Surfaces written by Kristopher Tapp and published by Springer. This book was released on 2016-09-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.
