**AMS Chelsea Publishing**

Volume: 341;
1962;
487 pp;
Hardcover

MSC: Primary 22; 53; 43;

Print ISBN: 978-0-8218-2735-2

Product Code: CHEL/341.H

List Price: $57.00

Individual Member Price: $51.30

**Electronic ISBN: 978-1-4704-2992-8
Product Code: CHEL/341.H.E**

List Price: $57.00

Individual Member Price: $51.30

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# Differential Geometry and Symmetric Spaces

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*Sigurdur Helgason*

Sigurdur Helgason's

Although much has happened in the field since the publication of this book, as
demonstrated by Helgason's own three-volume expansion of the original work,
this single volume is still an excellent overview of the subjects. For
instance, even though there are now many competing texts, the chapters on
differential geometry and Lie groups continue to be among the best treatments
of the subjects available. There is also a well-developed treatment of
Cartan's classification and structure theory of symmetric spaces. The last
chapter, on functions on symmetric spaces, remains an excellent introduction to
the study of spherical functions, the theory of invariant differential
operators, and other topics in harmonic analysis. This text is rightly called a
classic.

Sigurdur Helgason was awarded the Steele Prize for

#### Table of Contents

# Table of Contents

## Differential Geometry and Symmetric Spaces

- Cover Cover11
- Title page iii4
- Contents v6
- Preface to the new printing ix10
- Preface xi12
- Elementary differential geometry 116
- Lie groups and Lie algebras 87102
- Structure of semisimple Lie algebras 130145
- Symmetric spaces 162177
- Decomposition of symmetric spaces 193208
- Symmetric spaces of the noncompact type 214229
- Symmetric spaces of the compact type 241256
- Hermitian symmetric spaces 281296
- On the classification of symmetric spaces 326341
- Functions on symmetric spaces 360375
- Bibliography 457472
- List of notational conventions 473488
- Symbols frequently used 476491
- Author index 479494
- Subject index 482497
- Reviews for the first edition 487502
- Back Cover Back Cover1506

#### Readership

Graduate students and research mathematicians interested in topological groups and Lie groups; mathematical physicists.

#### Reviews

Remarkably well written … might be used as a textbook for how to write mathematics.

-- Bulletin of the AMS