An Introduction to Differentiable Manifolds and Riemannian Geometry (Pure and Applied Mathematics, Volume 120) (Paperback)

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Key Phrases: contracting mapping theorem, single coordinate neighborhood, regular submanifold, Theorem Let, Proof Let, Example Let (more...)

Editorial Reviews

Product Description

This book was planned and written as a text for a two-semester course designed, it is hoped, to overcome, or at least to minimize, some of these difficulties. It has, in fact, been used successfully several times in preliminary form as class notes for a two-semester course intended to lead the student from a reasonable mastery of advanced (multivariable) calculus and a rudimentary knowledge of differentiable manifolds, including some facility in working with the basic tools of manifold theory: tensors, differential forms, Lie and covariant derivatives, multiple integrals, and so on. Although in overall content this book necessarily overlaps the several available excellent books on manifold theory, there are differences in presentation and emphasis which, it is hoped, will make it particularly suitable as an introductory text.

From the Back Cover

Differentiable manifolds abd the differential and integral calculus of their associated structures, such as vectors, tensors, and differential forms are of great importance in many areas of mathematics and its applications. Although basically and extension of advanced, or multivariable calculus, the leap from Euclidean space to manifolds can often be difficult. It takes time and patience, and it is easy to become mirred in abstraction and generalization.
In this text the author draws on his extensive experience in teaching this subject to minimize these difficulties. The pace is relatively liesurely, inessential abstraction and generality are avoided, the essential ideas used from the prerequisite subjects are reviewed, and there is an abundance of accessible and carefully developed examples to illuminate new concepts and to motivate the reader by illustrating their power. There are more than 400 exercises for the reader.
This book has been in constant, successful use for more than 25 years and has helped several generations of students as well as working mathemeticians, physicists and engineers to gain a good working knowledge of manifolds and to appreciate their importance, beauty and extensive applications. --This text refers to an alternate Paperback edition.

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Product Details

• Paperback: 424 pages
• Publisher: Academic Press; 2 edition (May 12, 1986)
• Language: English
• ISBN-10: 012116053X
• ISBN-13: 978-0121160531
• Product Dimensions: 8.9 x 6.1 x 0.8 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (5 customer reviews)
• Amazon.com Sales Rank: #1,210,524 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

12 of 12 people found the following review helpful:

5.0 out of 5 stars This is a book for REAL mathematicians, April 16, 2005

By	T. Baillie Arnold (Brunswick, ME) - See all my reviews (REAL NAME)

This review is from: An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) (Paperback)

This book is an wonderful introduction to Differential Geometry for the serious student of mathematics. However, it is not aimed at engineers, physicists or even applied mathaticians.
The author assumes the reader has an extensive knowledge of abstract algebra and at least one course in analysis. Likewise, he has chosen to emphasis applications of the subject to Lie Groups, homotopy theory, and group actions, rather than the physical applications that applied mathematicians are looking for. But, for the student of pure mathematics, this text is a great starting point into the rich world of differential geometry.
Also, while this book is an introduction and requires no previous knowledge of the subject, it covers enough ground to be followed up by such topics as the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, or Morse Theory.

18 of 20 people found the following review helpful:

4.0 out of 5 stars Very Nice Nontrivial Introduction, May 31, 2000

By	Kevin R. Vixie (Los Alamos, NM) - See all my reviews (REAL NAME)

This book is a careful treatment of the subjects in the title. It is an introduction, but it manages to cover quite a bit of ground with lots of examples to illustrate. One of it's distinguishing points is the way in which the concrete, coordinate based calculations are emphasized even while usually presenting the more abstract, coordinate free approach as well.

The book does a good job at stimulating those studying it to develop intuition. I found the book helpful when I was first studying the subject.

14 of 19 people found the following review helpful:

5.0 out of 5 stars great introductory text, March 27, 2002

By	Alex "supermanifold" (MTL) - See all my reviews

My first course on manifolds was based on this book, and I believe that it is the best introduction to the subject (especially for beginners). I thoroughly enjoyed it! I should also recommend Conlon's 'Differentiable Manifolds' (2ed, Birkhauser), as it is the perfect follow-up to Boothby. --A