Differential Geometry, Lie Groups and

The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful.

Elementary Differential Geometry
Lie Groups and Lie Algebras
Structure of Semisimple Lie Algebras
Symmetric Spaces
Decomposition of Symmetric Spaces
Symmetric Spaces of the Noncompact Type
Symmetric Spaces of the Compact Type
Hermitian Symmetric Spaces
Structure of Semisimple Lie Groups
The Classification of Simple Lie Algebras and of Symmetric Spaces
Solutions to Exercises
Some Details
Bibliography
List of Notational Conventions
Symbols Frequently Used
Index
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Differential Geometry, Lie Groups and Symmetric Spaces

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