Customer Reviews

Differential Geometric Structures (Dover Books on Mathematics)

5 star:		(3)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

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.

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.

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.

I have been using this book from the First edition.
I consider it a very useful book for a Differential Geometer
The treatment of parallel transport is hard to find in other books of the same
level.
Also it has been very helful as a reference when we have been using a different
book. Sometimes, the expositions on connections is too dogmatic and you do NOT see
the important idea behind the "abstract" definition.This book fill a gap.
I liked the treatment of "Lie group structures in Spheres" difficult to find in
most of simimilar books.
I general is a book that I recomend and it has been appretiated by several geometers friends

this book is not for engineers, there is no introduction to those
topics mentioned, if you do not have some mathematical background on manifolds etc, the book will not help you. i m giving 4 stars
just to warn the engineers like me trying to get into differential geometry.