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.

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 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 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 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 257 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.

Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

Download or read book Ruled Varieties written by Gerd Fischer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable. This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necessary techniques are developed, especially concerning Grassmannians and fundamental forms in a version suitable for complex projective algebraic geometry. Finally, this leads to recent results on the classification of developable ruled varieties and facts about tangent and secant varieties. Compared to many other topics of algebraic geometry, this is an area easily accessible to a graduate course.

Download or read book Undergraduate Algebraic Geometry written by Miles Reid and published by Cambridge University Press. This book was released on 1988-12-15 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.

Download or read book Projective and Cayley Klein Geometries written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction into projective geometry. The first part presents n-dimensional projective geometry over an arbitrary skew field; the real, the complex, and the quaternionic geometries are the central topics, finite geometries playing only a minor part. The second deals with classical linear and projective groups and the associated geometries. The final section summarizes selected results and problems from the geometry of transformation groups.

Download or read book Projective Duality and Homogeneous Spaces written by Evgueni A. Tevelev and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.

Download or read book Basic Algebraic Geometry 2 written by Igor Rostislavovich Shafarevich and published by Springer Science & Business Media. This book was released on 1994 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics.

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.

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 Algebraic Geometry I written by V.I. Danilov and published by Springer Science & Business Media. This book was released on 1998-03-17 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: "... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum

Download or read book Complex Geometry written by Daniel Huybrechts and published by Springer Science & Business Media. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Download or read book Projective Geometry written by T. Ewan Faulkner and published by Courier Corporation. This book was released on 2013-02-20 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960 edition.

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.