Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics) - Hardcover

Helgason, Sigurdur

Hardcover

ISBN 10: 0821828487 ISBN 13: 9780821828489

Publisher: Amer Mathematical Society, 2001

Synopsis

A ninth printing of Helgason's 1978 textbook and reference published by Academic Press, itself a revision of and sequel to his 1962 Differential Geometry and Symmetric Spaces , based in turn on lectures he gave a the University of Chicago in 1958 and later at Columbia and MIT. He begins by explaining differential geometry, emphasizing Riemannian geometry, then applies that to the basic theory of Lie groups and Lie algebras. A two-volume sequence, Groups and Geometric Analysis and Geometric Analysis on Symmetric Spaces have been published in the Society's series Mathematical Surveys and Monographs. Annotation c. Book News, Inc., Portland, OR (booknews.com)

About this title

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

Review

"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

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2001
• Language: English
• ISBN 10: 0821828487
• ISBN 13: 9780821828489
• Binding: Hardcover
• Edition number: 1
• Number of pages: 640