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Spaces of Constant Curvature: Sixth Edition
 
Joseph A. Wolf University of California, Berkeley, Berkeley, CA
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7365-5
Product Code:  CHEL/372.H.S
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $54.00
eBook ISBN:  978-1-4704-1579-2
Product Code:  CHEL/372.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-1-4704-7365-5
eBook: ISBN:  978-1-4704-1579-2
Product Code:  CHEL/372.H.S.B
List Price: $125.00 $92.50
MAA Member Price: $112.50 $83.25
AMS Member Price: $106.00 $83.25
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Spaces of Constant Curvature: Sixth Edition
Joseph A. Wolf University of California, Berkeley, Berkeley, CA
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7365-5
Product Code:  CHEL/372.H.S
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $54.00
eBook ISBN:  978-1-4704-1579-2
Product Code:  CHEL/372.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-1-4704-7365-5
eBook ISBN:  978-1-4704-1579-2
Product Code:  CHEL/372.H.S.B
List Price: $125.00 $92.50
MAA Member Price: $112.50 $83.25
AMS Member Price: $106.00 $83.25
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 3722011; 420 pp
    MSC: Primary 53; 20; 22; Secondary 14; 17;

    This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups.

    Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford–Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.

    Readership

    Graduate students and research mathematicians interested in riemannian geometry and homogeneous spaces of Lie groups.

  • Table of Contents
     
     
    • Riemannian geometry
    • Chapter 1. Affine differential geometry
    • Chapter 2. Riemannian curvature
    • The Euclidean space form problem
    • Chapter 3. Flat Riemannian manifolds
    • The spherical space form problem
    • Chapter 4. Representations of finite groups
    • Chapter 5. Vincent’s work on the spherical space form problem
    • Chapter 6. The classification of fixed point free groups
    • Chapter 7. The solution to the spherical space form problem
    • Space form problems on symmetric spaces
    • Chapter 8. Riemannian symmetric spaces
    • Chapter 9. Space forms of irreducible symmetric spaces
    • Chapter 10. Locally symmetric spaces of non-negative curvature
    • Space form problems on indefinite metric manifolds
    • Chapter 11. Spaces of constant curvature
    • Chapter 12. Locally isotropic manifolds
    • Appendix to Chapter 12
  • Additional Material
     
     
  • 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: 3722011; 420 pp
MSC: Primary 53; 20; 22; Secondary 14; 17;

This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups.

Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford–Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.

Readership

Graduate students and research mathematicians interested in riemannian geometry and homogeneous spaces of Lie groups.

  • Riemannian geometry
  • Chapter 1. Affine differential geometry
  • Chapter 2. Riemannian curvature
  • The Euclidean space form problem
  • Chapter 3. Flat Riemannian manifolds
  • The spherical space form problem
  • Chapter 4. Representations of finite groups
  • Chapter 5. Vincent’s work on the spherical space form problem
  • Chapter 6. The classification of fixed point free groups
  • Chapter 7. The solution to the spherical space form problem
  • Space form problems on symmetric spaces
  • Chapter 8. Riemannian symmetric spaces
  • Chapter 9. Space forms of irreducible symmetric spaces
  • Chapter 10. Locally symmetric spaces of non-negative curvature
  • Space form problems on indefinite metric manifolds
  • Chapter 11. Spaces of constant curvature
  • Chapter 12. Locally isotropic manifolds
  • Appendix to Chapter 12
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
Please select which format for which you are requesting permissions.