Projective Differential Geometry
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Projective Differential Geometry Of Submanifolds
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Author : M.A. Akivis
language : en
Publisher: Elsevier
Release Date : 1993-06-30
Projective Differential Geometry Of Submanifolds written by M.A. Akivis and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-30 with Mathematics categories.
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.
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.
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.
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.
Projective Differential Geometry Of Curves And Surfaces
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Author : Ernest Preston Lane
language : en
Publisher:
Release Date : 2012
Projective Differential Geometry Of Curves And Surfaces written by Ernest Preston Lane and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Geometry, Differential categories.
C Projective Geometry
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Author : David M Calderbank
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
C Projective Geometry written by David M Calderbank and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
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.
Algebraic Geometry And Projective Differential Geometry
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Author : J. M. Landsberg
language : en
Publisher:
Release Date : 1999
Algebraic Geometry And Projective Differential Geometry written by J. M. Landsberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Geometry, Algebraic categories.
Projective Differential Geometry Of Curves And Ruled Surfaces
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Author : E. J. Wilczynski
language : en
Publisher:
Release Date : 1905
Projective Differential Geometry Of Curves And Ruled Surfaces written by E. J. Wilczynski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1905 with Geometry, Algebraic categories.
Projective Differential Geometry And Linear Homogeneous Differential Equations
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Author : Takeshi Sasaki
language : en
Publisher:
Release Date : 1999
Projective Differential Geometry And Linear Homogeneous Differential Equations written by Takeshi Sasaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Projective differential geometry categories.
Projective Differential Geometry Of Curves And Ruled Surfaces
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Author : E J 1876-1932 Wilczynski
language : de
Publisher: Legare Street Press
Release Date : 2022-10-27
Projective Differential Geometry Of Curves And Ruled Surfaces written by E J 1876-1932 Wilczynski and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with categories.
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