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Differential Geometry, Lie Groups, and Symmetric Spaces, Volume 80 (Pure and Applied Mathematics), by Sigurdur Helgason
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The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful.
- Sales Rank: #2515716 in Books
- Published on: 1979-01-11
- Original language: English
- Number of items: 1
- Dimensions: 9.50" h x 6.50" w x 1.25" l,
- Binding: Hardcover
- 628 pages
Review
A great book. A necessary item in any mathematical library. -- S.S. Chern, Scripta Mathematica, 1963
An instant classic. -- A. Koranyi, American Scientist, 1985
Impressive skill and force in developing the needed background in manifold theory and algebra, giving crisp and accessible proofs of the major results--required reading for anyone interested in Lie group theory, pure or applied. -- R. Hermann, SIAM Review
The exposition is brilliant - might be used as a text for 'how to write mathematics'. -- L. Auslander, Bulletin of the American Mathematical Society, 1964
From the Publisher
The author was awarded "The Steele Prize" of the American Mathematical Society 1988 for this book, together with an accompanying volume, "Groups and Geometric Analysis" Academic Press, 1984
Most helpful customer reviews
0 of 1 people found the following review helpful.
Four Stars
By Acacio Bizarria Neves
Muito bom esse livro, recomendo.
21 of 23 people found the following review helpful.
Unsurpassed, but demanding
By Jim Curry
As I reviewed this book at Amazon, I found only one review, which I considered to be too harsh. You should understand that Helgason is writing a graduate textbook. Students will learn about "modules" in their graduate algebra course. They will learn De Rham's theorem in an introductory analysis course or sometimes even in a topology course (yes, it can happen). So, most of the language for which another reviewer criticized him would usually be covered in other graduate courses.
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.
3 of 4 people found the following review helpful.
Helgason Differential Geometry
By Lucius Schoenbaum
I'm not qualified to say much about this book, but I think it's excellent and thought it deserved a higher amazon rating. Besides being remarkably clear (much like the cold air of Helgason's home country of Iceland), I think it's a great, wonderful bridge between the original works in Lie theory and the more basic textbook treatments of DG and Lie theory out there (Warner, do Carmo, Lee, ...), many of which are quite good. It is filled with references and citations to original papers (some by the author) and is perhaps more connected to the historical genesis of the subject than other textbooks.
"A great book... a necessary item in any mathematical library." -S.S. Chern
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