Differential Geometric Structures (Dover Books on Mathematics) (Paperback)

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Editorial Reviews

Product Description

Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Product Details

• Paperback: 352 pages
• Publisher: Dover Publications; Dover Ed edition (June 5, 2007)
• Language: English
• ISBN-10: 048645844X
• ISBN-13: 978-0486458441
• Product Dimensions: 9.1 x 6 x 0.8 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon.com Sales Rank: #772,484 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

16 of 18 people found the following review helpful:

3.0 out of 5 stars Peculiar, June 5, 2008

By	Gadjo Dilo (Canada) - See all my reviews

This book contains material about differential geometry that is very hard to find in any other book, if possible at all. However for people who feel uncomfortable with different approaches of what they already know, a word of warning is in order: the book builds everything on 5 axioms about parallel structures in bundles. All other approaches (frame bundles, connections e.t.c.) are deduced later in the book. Five axioms might take a hard-swallowing and the trade-off is that they mimic the intuition for Euclidean spaces. Of course any serious reader will not expect to learn differential geometry from one book, so overall it is a useful addition to your collection. Finally, looking at the size of the book and the material it covers you can expect the text to be pretty dense and this is actually the case. Several books on smooth manifolds are suggested in the beginning as companions and Warner's book, which is cited consistently for background results, is a prerequisite for this book.

12 of 17 people found the following review helpful:

5.0 out of 5 stars the best intro to diff. geom. ever -- period, July 22, 2007

By	Phillip E. Parker "Dogtown Geometry Shoal" (Wichita St. U.) - See all my reviews (REAL NAME)

I have been recommending this book to my colleagues and students since 1981. Finally, they can get a copy easily.

Prequisites are modest, and should be part of the standard math graduate curriculum anyway: the equivalent of Chapters 1 --3 of Warner (differential manifolds, tensors and forms, and a minimal introduction to Lie groups).

Given these, it is simply the best introduction ever written.

9 of 14 people found the following review helpful:

5.0 out of 5 stars Finally in print again, September 26, 2007

By	David Fisher (Indiana University, Bloomington) - See all my reviews (REAL NAME)

I learned a great deal from this book
in my second year of grad school and
have recommended it to dozens of people
since then. It is wonderful to see it
back in print. A fantastic introduction
to differential geometry.