Differential geometry and symmetric spaces / Sigurdur Helgason.

Format:

Book

Author/Creator:

Helgason, Sigurdur, 1927- author.

Series:

AMS Chelsea Publishing Series

AMS Chelsea Publishing, v. 341

Language:

English

Subjects (All):

Geometry, Differential.

Symmetric spaces.

Physical Description:

1 online resource (506 pages)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : AMS Chelsea Publishing, 2001.

Summary:

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.

Contents:

Cover

Title page

Contents

Preface to the new printing

Preface

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

On the classification of symmetric spaces

Functions on symmetric spaces

Bibliography

List of notational conventions

Symbols frequently used

Author index

Subject index

Reviews for the first edition

Back Cover.

Notes:

Originally published: New York : Academic Press, 1962.

Includes bibliographical references and indexes.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-2992-6

OCLC:

982023532