Synthetic Geometry Of Manifolds
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Synthetic Geometry Of Manifolds
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2010
Synthetic Geometry Of Manifolds written by Anders Kock 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 2010 with Mathematics categories.
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
Synthetic Differential Geometry
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-22
Synthetic Differential Geometry written by Anders Kock 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 2006-06-22 with Mathematics categories.
This book, first published in 2006, details how limit processes can be represented algebraically.
Algebraic Geometry Over C Infinity Rings
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Author : Dominic D. Joyce
language : en
Publisher:
Release Date : 2019
Algebraic Geometry Over C Infinity Rings written by Dominic D. Joyce and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Differentiable functions categories.
Lectures On Symplectic Geometry
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Author : Ana Cannas da Silva
language : en
Publisher: Springer
Release Date : 2004-10-27
Lectures On Symplectic Geometry written by Ana Cannas da Silva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-27 with Mathematics categories.
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Foliations On Riemannian Manifolds And Submanifolds
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Author : Vladimir Rovenski
language : en
Publisher: Birkhäuser
Release Date : 1997-12-29
Foliations On Riemannian Manifolds And Submanifolds written by Vladimir Rovenski and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-29 with Mathematics categories.
This monograph is based on the author's results on the Riemannian ge ometry of foliations with nonnegative mixed curvature and on the geometry of sub manifolds with generators (rulings) in a Riemannian space of nonnegative curvature. The main idea is that such foliated (sub) manifolds can be decom posed when the dimension of the leaves (generators) is large. The methods of investigation are mostly synthetic. The work is divided into two parts, consisting of seven chapters and three appendices. Appendix A was written jointly with V. Toponogov. Part 1 is devoted to the Riemannian geometry of foliations. In the first few sections of Chapter I we give a survey of the basic results on foliated smooth manifolds (Sections 1.1-1.3), and finish in Section 1.4 with a discussion of the key problem of this work: the role of Riemannian curvature in the study of foliations on manifolds and submanifolds.
Computational Synthetic Geometry
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Author : Jürgen Bokowski
language : en
Publisher: Springer
Release Date : 2006-11-14
Computational Synthetic Geometry written by Jürgen Bokowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.
On The Hypotheses Which Lie At The Bases Of Geometry
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Author : Bernhard Riemann
language : en
Publisher: Birkhäuser
Release Date : 2016-04-19
On The Hypotheses Which Lie At The Bases Of Geometry written by Bernhard Riemann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Geometry And Topology
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Author : Miles Reid
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-10
Geometry And Topology written by Miles Reid 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 2005-11-10 with Mathematics categories.
Geometry aims to describe the world around us. It is central to many branches of mathematics and physics, and offers a whole range of views on the universe. This is an introduction to the ideas of geometry and includes generous helpings of simple explanations and examples. The book is based on many years teaching experience so is thoroughly class-tested, and as prerequisites are minimal, it is suited to newcomers to the subject. There are plenty of illustrations; chapters end with a collection of exercises, and solutions are available for teachers.
Differential Geometry Riemannian Geometry
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Differential Geometry Riemannian Geometry written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The third of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 3 begins with an overview by R.E. Greene of some recent trends in Riemannia
A Panoramic View Of Riemannian Geometry
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Author : Marcel Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Panoramic View Of Riemannian Geometry written by Marcel Berger 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.
Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way, following in particular Gauss and Riemann.