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Riemannian Manifolds: An Introduction to Curvature (Graduate Texts in Mathematics), by John M. Lee
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This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
- Sales Rank: #320827 in Books
- Published on: 1997-09-23
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .55" w x 6.10" l, .77 pounds
- Binding: Paperback
- 226 pages
Most helpful customer reviews
24 of 26 people found the following review helpful.
The printing is not up to the standard of the writing
By Christopher Grant
By all accounts, this and Dr. Lee's other two books on manifolds are exceptionally well-written. But my copies arrived from Amazon this week, and, unfortunately, Amazon and Springer have decided to replace the crisp offset-printing of earlier printings by lower quality digitally-printed versions, probably as a cost-cutting measure.
If you care about how books look, I'd suggest trying Amazon marketplace or small retailers elsewhere to increase your odds of getting a superior copy from an earlier printing.
17 of 18 people found the following review helpful.
Do Carmo's is better
By i-review98
I've taught an introductory differential geometry course from Lee's book, and in retrospect Do Carmo's "Riemannian Geometry" would have been a better choice. To be fair Lee does masterful job introducing basic concepts from curvature to Jacobi fields, but here are a few things I disliked. The book assumes working knowledge of smooth manifolds and Lie brackets, while many students need review of the former, and know nothing of the latter. Lee doesn't give enough examples beyond constant curvature spaces: there is virtually no mention of warped products, Riemannian submersions, Lie groups, or homogeneous spaces. Exercises are few, unmotivated, and their difficulty is in stark contrast with the easiness of the main text. I feel Do Carmo's book is superior in all respects, and last time I checked it was not much more expensive.
11 of 11 people found the following review helpful.
Nice graduate text.
By David A. Glickenstein
I used this book to teach about half a year of a graduate Riemannian manifolds course. It is a very good introductory text. I wish it has a bit more background on curves and surfaces, but otherwise it was excellent. It doesn't get into a lot of more advanced topics, but the treatment of Jacobi fields and so forth is really good.
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