Differential Geometry and Symmetric Spaces

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 on Riemannian geometry and for the analysis and geometry of symmetric spaces still offers a clear overview of the subjects. The text includes a well-developed treatment of Cartan's classification and structure theory of symmetric spaces, and the last chapter, on functions on symmetric spaces, remains a comprehensive introduction to the study of spherical functions, the theory of invariant differential operators, and other topics in harmonic analysis.