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.
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21 of 25 people found the following review helpful:
3.0 out of 5 stars
Peculiar,
By Gadjo Dilo (Canada) - See all my reviews
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This review is from: Differential Geometric Structures (Dover Books on Mathematics) (Paperback)
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.
16 of 23 people found the following review helpful:
5.0 out of 5 stars
the best intro to diff. geom. ever -- period,
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This review is from: Differential Geometric Structures (Dover Books on Mathematics) (Paperback)
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.
10 of 15 people found the following review helpful:
5.0 out of 5 stars
Finally in print again,
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This review is from: Differential Geometric Structures (Dover Books on Mathematics) (Paperback)
I learned a great deal from this bookin 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.
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