Includes bibliographical references (p. -404) and index.
|Series||Birkhäuser advanced texts|
|LC Classifications||QA614.3 .C66 2001|
|The Physical Object|
|Pagination||xii, 418 p. :|
|Number of Pages||418|
|ISBN 10||0817641343, 3764341343|
|LC Control Number||2001025140|
Apr 07, · The heart of the book is Chapter VI, where the concept of gluing manifolds together is explored. Normally, connected sums are defined by removing imbedded balls in 2 closed manifolds and gluing them along the spherical boundaries, but Kosinski instead /5(6). Jan 12, · The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of cyrusofficial.com by: Differentiable manifolds are a generalisation of surfaces. Unlike the latter, however, we need not imagine a manifold as being immersed in a higher-dimensional space in order to study its geometric properties. In this chapter and the next, we define differentiable manifolds and build the basics to do calculus on them. “The purpose of this book is to present some fundamental notions of differentiable geometry of manifolds and some applications in physics. The topics developed in the book are of interest of advanced undergraduate and graduate students in mathematics and physics. The author succeeded to connect differential geometry with mechanics.
Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. 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 understandingAuthor: Georges de Rham. This book is a good introduction to manifolds and lie groups. Still if you dont have any background,this is not the book to start cyrusofficial.com first chapter is about the basics of manifolds:vector fields,lie brackts,flows on manifolds and more, this chapter can help one alot as a second book on the cyrusofficial.com by: 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 .
Warner's Foundations of Differentiable Manifolds is an 'older' classic. Javier already mentioned Jeffrey Lee's 'Manifolds and Differential Geometry' and Nicolaescu's very beautiful book. I'd like to add: Conlon - Differentiable Manifolds. Isham - Modern Differential Geometry for Physicists. Morita - Geometry of Differential Forms. "The book under review is a new, enlarged and somewhat revised edition of the author’s successful textbook Differentiable Manifolds (A first course) published also by Birkhäuser in Mathematicians already familiar with the earlier edition have spoken very favourably about the contents and the lucidity of the expositionAuthor: Lawrence Conlon. An Introductory Course on Differentiable Manifolds book. Read 2 reviews from the world's largest community for readers. Based on author Siavash Shahshaha 5/5. Dec 06, · 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.