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Differential Geometry and Symmetric Spaces
 
Sigurdur Helgason Massachusetts Institute of Technology, Cambridge, MA
Differential Geometry and Symmetric Spaces
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7687-8
Product Code:  CHEL/341.H.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-2992-8
Product Code:  CHEL/341.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-1-4704-7687-8
eBook: ISBN:  978-1-4704-2992-8
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
Differential Geometry and Symmetric Spaces
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Differential Geometry and Symmetric Spaces
Sigurdur Helgason Massachusetts Institute of Technology, Cambridge, MA
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7687-8
Product Code:  CHEL/341.H.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-2992-8
Product Code:  CHEL/341.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-1-4704-7687-8
eBook ISBN:  978-1-4704-2992-8
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 Details
     
     
    AMS Chelsea Publishing
    Volume: 3411962; 487 pp
    MSC: 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 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 Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces.

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3411962; 487 pp
MSC: 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 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 Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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