Differential Geometry and Symmetric Spaces
About this Title
Sigurdur Helgason, Massachusetts Institute of Technology, Cambridge, MA
Publication: AMS Chelsea Publishing
Publication Year: 1962; Volume 341
ISBNs: 978-0-8218-2735-2 (print); 978-1-4704-2992-8 (online)
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.
Graduate students and research mathematicians interested in topological groups and Lie groups; mathematical physicists.
Table of Contents
- 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