Customer Reviews

Riemannian Geometry: A Beginners Guide, Second Edition

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

 

 

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.

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.

I wish I had read these reviews before my purchase. I was disappointed in this book. It is certainly no beginners guide. I found the author's chapter on Relativity to be un-inspiring. This book is clearly intended as a review of the material for persons already familiar with the mathematics of it. He even admits as much in his introduction. Successful geometers who wish to have a bird's eye view of the complex material or wish to gain knowledge of future study areas within diff. geometry are recommened to this book.

As other reviewers have written, this book is too terse to serve as a standalone introduction to Riemannian geometry. It lacks some definitions and explanations of basic concepts, and often tries to do too much too fast. The author has an intuitive approach that I enjoy a lot, but the analogies and figures aren't enough to fill the technical gaps in the exposition.

With more details, this could've been a fantastic introductory book.

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.

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!