Geometria Diferencial Varietats Diferenciables I Varietats De Riemann
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Geometria Diferencial Varietats Diferenciables I Varietats De Riemann
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Author : Carlos Currás Bosch
language : ca
Publisher: Edicions Universitat Barcelona
Release Date : 2003-04-28
Geometria Diferencial Varietats Diferenciables I Varietats De Riemann written by Carlos Currás Bosch and has been published by Edicions Universitat Barcelona this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-28 with categories.
Es dóna una introducció als aspectes fonamentals de la geometria diferencial. En la primera part, es tracten aspectes bàsics de les varietats diferenciables, fent atenció especial al càlcul tensorial. En la segona part, es veuen qüestions més destacables de les varietats de Riemann: immersions geomètriques, fórmules de variació, teoremes de comparació; i es desenvolupen els temes tractats. Hi ha el recolzament de problemes a diversos capítols. Es un llibre indicat per a estudiants que hagin seguit cursos d'àlgebra lineal, càlcul infinitesimal i topologia elemental, en ciències matemàtiques o física, o tècnics de nivell superior.
An Introduction To Differentiable Manifolds And Riemannian Geometry
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Author : William M. Boothby
language : en
Publisher:
Release Date : 1997
An Introduction To Differentiable Manifolds And Riemannian Geometry written by William M. Boothby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Differential Manifolds
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential Manifolds 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 volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different contexts. The foreword which I wrote in the earlier book is still quite valid and needs only slight extension here. Between advanced calculus and the three great differential theories (differential topology, differential geometry, ordinary differential equations), there lies a no-man's-land for which there exists no systematic exposition in the literature. It is the purpose of this book to fill the gap. The three differential theories are by no means independent of each other, but proceed according to their own flavor. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.). One may also use differentiable structures on topological manifolds to determine the topological structure of the manifold (e.g. it la Smale [26]).
Differential And Riemannian Manifolds
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential And Riemannian Manifolds 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.
This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. 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 differentiable maps in them (immersions, embeddings, isomorphisms, etc.).
An Introduction To Differentiable Manifolds And Riemannian Geometry
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Author : William Munger Boothby
language : en
Publisher:
Release Date : 1975
An Introduction To Differentiable Manifolds And Riemannian Geometry written by William Munger Boothby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Differential Manifolds
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Author : Antoni A. Kosinski
language : en
Publisher: Courier Corporation
Release Date : 2013-07-02
Differential Manifolds written by Antoni A. Kosinski and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.
Differentiable Manifolds
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Author : Georges de Rham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differentiable Manifolds written by Georges de Rham 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.
In this work, I have attempted to give a coherent exposition of the theory of differential forms on a manifold and harmonic forms on a Riemannian space. The concept of a current, a notion so general that it includes as special cases both differential forms and chains, is the key to understanding how the homology properties of a manifold are immediately evident in the study of differential forms and of chains. The notion of distribution, introduced by L. Schwartz, motivated the precise definition adopted here. In our terminology, distributions are currents of degree zero, and a current can be considered as a differential form for which the coefficients are distributions. The works of L. Schwartz, in particular his beautiful book on the Theory of Distributions, have been a very great asset in the elaboration of this work. The reader however will not need to be familiar with these. Leaving aside the applications of the theory, I have restricted myself to considering theorems which to me seem essential and I have tried to present simple and complete of these, accessible to each reader having a minimum of mathematical proofs background. Outside of topics contained in all degree programs, the knowledge of the most elementary notions of general topology and tensor calculus and also, for the final chapter, that of the Fredholm theorem, would in principle be adequate.
Ricci Flow And Geometric Applications
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Author : Michel Boileau
language : en
Publisher: Springer
Release Date : 2016-09-09
Ricci Flow And Geometric Applications written by Michel Boileau and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-09 with Mathematics categories.
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.
Differentiable Manifolds
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Author : Shiing-Shen Chern
language : en
Publisher:
Release Date : 1959
Differentiable Manifolds written by Shiing-Shen Chern and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Differentiable manifolds categories.
Old And New Aspects In Spectral Geometry
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Author : M.-E. Craioveanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Old And New Aspects In Spectral Geometry written by M.-E. Craioveanu 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 2013-03-14 with Mathematics categories.
It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.