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Softcover ISBN:  9781470473655 
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Softcover ISBN:  9781470473655 
Product Code:  CHEL/372.H.S 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $54.00 
eBook ISBN:  9781470415792 
Product Code:  CHEL/372.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9781470473655 
eBook ISBN:  9781470415792 
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 DetailsAMS Chelsea PublishingVolume: 372; 2011; 420 ppMSC: 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 pseudoriemannian 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 pseudoriemannian 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 pseudoriemannian 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 pseudoriemannian symmetric spaces. Additional references have been added to this sixth edition as well.
ReadershipGraduate 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 nonnegative 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

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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 pseudoriemannian 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 pseudoriemannian 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 pseudoriemannian 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 pseudoriemannian symmetric spaces. Additional references have been added to this sixth edition as well.
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 nonnegative curvature

Space form problems on indefinite metric manifolds

Chapter 11. Spaces of constant curvature

Chapter 12. Locally isotropic manifolds

Appendix to Chapter 12