Softcover ISBN:  9781470476878 
Product Code:  CHEL/341.H.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470429928 
Product Code:  CHEL/341.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470476878 
eBook: ISBN:  9781470429928 
Product Code:  CHEL/341.H.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Softcover ISBN:  9781470476878 
Product Code:  CHEL/341.H.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470429928 
Product Code:  CHEL/341.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470476878 
eBook ISBN:  9781470429928 
Product Code:  CHEL/341.H.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 341; 1962; 487 ppMSC: Primary 22; 53; 43
Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail.
Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own threevolume 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 welldeveloped 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 Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces.
ReadershipGraduate students and research mathematicians interested in topological groups and Lie groups; mathematical physicists.

Table of Contents

Chapters

Chapter 1. Elementary differential geometry

Chapter 2. Lie groups and Lie algebras

Chapter 3. Structure of semisimple Lie algebras

Chapter 4. Symmetric spaces

Chapter 5. Decomposition of symmetric spaces

Chapter 6. Symmetric spaces of the noncompact type

Chapter 7. Symmetric spaces of the compact type

Chapter 8. Hermitian symmetric spaces

Chapter 9. On the classification of symmetric spaces

Chapter 10. Functions on symmetric spaces


Reviews

Remarkably well written ... might be used as a textbook for how to write mathematics.
Bulletin of the AMS


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Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail.
Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own threevolume 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 welldeveloped 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 Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces.
Graduate students and research mathematicians interested in topological groups and Lie groups; mathematical physicists.

Chapters

Chapter 1. Elementary differential geometry

Chapter 2. Lie groups and Lie algebras

Chapter 3. Structure of semisimple Lie algebras

Chapter 4. Symmetric spaces

Chapter 5. Decomposition of symmetric spaces

Chapter 6. Symmetric spaces of the noncompact type

Chapter 7. Symmetric spaces of the compact type

Chapter 8. Hermitian symmetric spaces

Chapter 9. On the classification of symmetric spaces

Chapter 10. Functions on symmetric spaces

Remarkably well written ... might be used as a textbook for how to write mathematics.
Bulletin of the AMS