Save Big On Open-Box & Used Products: Buy "Differential Geometry, Lie Groups, and Symmetric S...” from Amazon Open-Box & Used and save 23% off the $84.00 list price. Product is eligible for Amazon's 30-day returns policy and Prime or FREE Shipping. See all offers from Amazon Open-Box & Used.
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter your mobile phone number.
Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics) F First Edition Edition
Use the Amazon App to scan ISBNs and compare prices.
Featured Springer resources in mathematics
Explore these featured titles in mathematics. Learn more
Frequently bought together
Customers who bought this item also bought
Special offers and product promotions
"This book has been famous for many years and used by several generations of readers. It is important that the book has again become available for a general audience." -- European Mathematical Society Newsletter
"One of the most important and excellent textbooks and a reference work about contemporary differential geometry ..." -- Zentralblatt MATH
"Important improvements in the new edition of S. Helgason's book will turn it into a desk book for many following generations." -- Mathematica Bohemica
"A great book ... a necessary item in any mathematical library." -- S. S. Chern, University of California
"Written with unmatched lucidity, systematically, carefully, beautifully." -- S. Bochner, Princeton University
"Helgason's monograph is a beautifully done piece of work and should be extremely useful for several years to come, both in teaching and in research." -- D. Spencer, Princeton University
"A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics." -- Barrett O'Neill, University of California
"Renders a great service in permitting the non-specialist, with a minimum knowledge of differential geometry and Lie groups, an initiation to the theory of symmetrical spaces." -- H. Cartan, Secretariat Mathématique, Paris
"The mathematical community has long been in need of a book on symmetric spaces. S. Helgason has admirably satisfied this need with his book, Differential Geometry and Symmetric Spaces. It is a remarkably well-written book ... a masterpiece of concise, lucid mathematical exposition ... it might be used as a textbook for "how to write mathematics"." -- Louis Auslander
"[The author] will earn the gratitude of many generations of mathematicians for this skillful, tasteful, and highly efficient presentation. It will surely become a classic." -- G. D. Mostow, Yale University
From the Publisher
If you are a seller for this product, would you like to suggest updates through seller support?
Top Customer Reviews
"A great book... a necessary item in any mathematical library." -S.S. Chern
As one reviewer said, this is a graduate text, so a certain amount of mathematical maturity and background is expected. My complaint is that if you have the maturity and background to reasonably understand the text, then you probably didn't need to read the text in the first place. To someone who already knows differential geometry and wants to get another perspective, or needs to jog his memory, I am sure Helgason's treatment is fine, though.
Overall, I found the book very confusing, since it is very terse, does not give examples or even explain the intuition or context behind a slew of definitions and theorems, and assumes what I think is an unreasonable amount of background and mathematical maturity. Also, I found many of the proofs hard to follow. To those not already comfortable with the material, I suggest turning elsewhere. In particular, I have found Warner Foundations of Differentiable Manifolds and Lie Groups very good for understanding much of the material in Helgason on Lie Groups and manifolds.
(As a disclaimer, I have only read chapters I and II since that is what we covered, but I suspect the style does not differ significantly between other parts of the book.)
Helgason writes tersely but extremely precisely. I know of no other author who gives similar sophistication of point of view and quick, to the point, proofs. He is a "best of breed," and I suppose that is part of the reason he has been a core member of the faculty at M.I.T. for such a long time. A serious student cannot really avoid reading the entire progression of these texts, particularly the "Groups and Geometric Analysis" title, perhaps second in the Helgason manuscripts.
I find the book difficult to follow from time to time, but I guess its because I barely finished Boothby's An intro to diff mfd and riemannian geometry. Yet as I hang on a little longer, I started to learn on multiple levels and even felt more confident about differential geometry as a result (before, I tried Nomizu and Kobayashi, but it didnt work for me). If you are also an engineer, I would highly recommend you to finish Boothby first (which would then require 1 or 2 companion books, such as Munkres and maybe Abraham, Marsden, Ratiu) and come back to read Ch 1&2. Ch3 on semi-simple lie algebra is a little demanding, so Humphrey might be a good first reading. The rest of the book is on symmetric spaces. I would recommend not to read them all but to read only what you need.
The only thing dissatisfying is that there are too few examples. But I guess its not a textbook anyway.