Riemannian Geometry: A Beginner's Guide - ISBN:0867202424

Riemannian Geometry: A Beginner's Guide

Date: 06 May 2011, 19:45

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Reviews
Summary: not a textbook
Rating: 3
Initially I wanted to use this book as the main textbook in a differential geometry course I were going to teach. It is relatively new, compare to do Carmo's, and it looks friendly, short, with some interesting material (hyperbolic spaces, relativity ...). But I were dissapointed after a few weeks. The arguments in this books are too shaky. I came to think that for a course in differential geometry of curves and surfaces, one of the main beauties, perhaps the primary one, is in providing solid, rigorous arguments for intuitive ideas. For this purpose do Carmo's book is still a better choice. This book could be used for motivational reading.
Summary: Nice book
Rating: 5
This book is a great companion to a more traditional textbook-this book does a very nice job of giving simple examples and motivations for some ideas in geometry...however, it would be good to have another textbook alongside it to fill in some gaps!
Summary: A nice easy going book.
Rating: 4
Can't agree with my friend from Ann Arbor. This is the most accesible book on Riemannian Geometry. Or to be precise, this is not even a book on Riemannian Geometry, It's only a guide! The author doesn't take the universal intrinsic approach to the subject, but only look at everything as a subspace of Eucleadean space, and see how those apparently extrinsically defined concepts indeed have intrinsic meannings. And that gives you a taste of the real part, which you must turn to some other books.
Summary: Riemannian Geometry - A Beginner's Guide
Rating: 2
Well I am only on page 10 and am considering quiting this book. I have a BSEE with quite a lot of mathematics history, but I know nothing about Riemann geometry. I got bogged down right from the beginning with this book. It's not that the material - so far - is that demanding, but the explanations are terse at best and some formulas seem to pop onto the page from hyperspace. Some variables are undefined, unfamiliar nomenclature is used without explanation and there is no exposition to show from where some rather complicated formula appear. Too much is assumed by the author for a book that claims to be a "beginners guide". You can waste a lot of time trying to guess what is on the authors mind.
I get the impression that by adding another 10 pages or so of elucidating math and text this might be a nice little survey of the subject matter, but as is I can't recommend it.
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