Projective Differential Geometry Old And New

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Projective Differential Geometry Old And New

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Author : Valentin Ovsienko
language : en
Publisher:
Release Date : 2005

Projective Differential Geometry Old And New written by Valentin Ovsienko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Projective differential geometry categories.

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. This book provides a rapid route for graduate students and researchers to contemplate the frontiers of contemporary research in this classic subject. The authors include exercises and historical and cultural comments relating the basic ideas to a broader context.

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.

Affine Differential Geometry

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Author : Katsumi Nomizu
language : en
Publisher: Cambridge University Press
Release Date : 1994-11-10

Affine Differential Geometry written by Katsumi Nomizu 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 1994-11-10 with Mathematics categories.

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.

Fundamentals Of Differential Geometry

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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Fundamentals Of Differential Geometry written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry. The size of the book influenced where to stop, and there would be enough material for a second volume (this is not a threat). At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differen tiable maps in them (immersions, embeddings, isomorphisms, etc. ). One may also use differentiable structures on topological manifolds to deter mine the topological structure of the manifold (for example, it la Smale [Sm 67]). In differential geometry, one puts an additional structure on the differentiable manifold (a vector field, a spray, a 2-form, a Riemannian metric, ad lib. ) and studies properties connected especially with these objects. Formally, one may say that one studies properties invariant under the group of differentiable automorphisms which preserve the additional structure. In differential equations, one studies vector fields and their in tegral curves, singular points, stable and unstable manifolds, etc. A certain number of concepts are essential for all three, and are so basic and elementary that it is worthwhile to collect them together so that more advanced expositions can be given without having to start from the very beginnings.

Perspectives On Projective Geometry

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Author : Jürgen Richter-Gebert
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-04

Perspectives On Projective Geometry written by Jürgen Richter-Gebert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-04 with Mathematics categories.

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.

Old And New Questions In Physics Cosmology Philosophy And Theoretical Biology

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Author : Alwyn Van der Merwe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Old And New Questions In Physics Cosmology Philosophy And Theoretical Biology written by Alwyn Van der Merwe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

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.

Linear And Projective Representations Of Symmetric Groups

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Author : Aleksandr Sergeevich Kleshchëv
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-30

Linear And Projective Representations Of Symmetric Groups written by Aleksandr Sergeevich Kleshchëv 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 2005-06-30 with Mathematics categories.

Kleshchev describes a new approach to the subject of the representation theory of symmetric groups.

Modern Approaches To The Invariant Subspace Problem

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Author : Isabelle Chalendar
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-18

Modern Approaches To The Invariant Subspace Problem written by Isabelle Chalendar 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 2011-08-18 with Mathematics categories.

One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.

Projective Differential Geometry Of Curves And Ruled Surfaces

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Author : Ernest Julius Wilczynski
language : en
Publisher:
Release Date : 1906

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 1906 with Curves categories.