Differential Geometry, Lie Groups, and Symmetric Spaces (Pure and Applied Mathematics,Vol 80): Sigurdur Helgason

Description

This is a considerably expanded version of the first 75% of the authors Differential Geometry and Symmetric Spaces, Academic Press 1962. For the graduate and advanced undergraduate students as well as mathematicians and mathematical physicists, the new book is both a self-contained text and a reference source on each of the three topics in the title.

The book provides an elementary introduction to differential geometry and to Lie groups and Lie algebras. It then focuses on the detailed structure theory of semisimple Lie groups and the geometry of symmetric spaces, ending with a complete classification. To facilitate self-study and to indicate further developments each chapter ends with "Exercises and Further Results". Solutions and references are given at the end of the book.

Review:
Superb Treatise and Indispensible Reference

The mere thought or mention of the name Helgason inspires respect and awe. This book gets five stars all the way on its merit alone, regardless of who wrote it. Difficult as it is, the book starts from the fundamentals and works up in a coherent logical manner, there are no gaps in his presentation. The negative review below is completely unjustified. If anyone would like to at least see some of what this book is like go to ocw.mit.edu and download Helgason's notes which use excerpts in this book. Some of the topics in this book are covered in a more easy going way in "Lie Groups, Lie Algebras, and Some of Their Applications" by Robert Gilmore. (If I'm not mistaken Gilmore was a student of Helgason.) This book is mathematical exposition at it's absolute finest and I don't think but 1 in 1,000 people reading this page need me to tell them that much less need a review to persuade them. This book has quite a reputation.

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