Customer Reviews

A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition

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Based on my reading of vol 1 and my browsing of vol 2 of this series, there is no doubt that Michael Spivak and differential geometry are a delightful combination. So I ordered vol 3-5 as well. And I learned that 90% of these three volumes is about A) the imbedding of manifolds in manifolds and B) the extrinsic properties of the imbedded manifold relative to the containing manifold. This is to be contrasted with vol 1-2, which is 90% about the intrinsic properties of a manifold. I found vol 3-5 of little interest to me as a physicist and not particularly interesting to me as a mathematician. So I returned the 3 volumes and spent the money on Araki's book on algebraic quantum field theory.

So, if imbedding manifolds does not excite you, I'm afraid that you should pass on these three volumes.

This is actually in response to the other review. Do Carmo has written two books on differential geometry and the previous commentator refers to only the undergraduate version. Riemannian geometry is the title of the other.
as for these, I personally find them too long to use except as a reference or when i'm confused. A real mathematician will get the detail of the proof and other technicalities on his or her own, so even if there are faults I find that any book with text of explaination and examples is worth it's weight. this is what makes it a five volume (as far as I know) set. i like it as a reference.