# Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)

## Sigurdur Helgason

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The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material.

Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbf{C}$ and Cartan's classification of simple Lie algebras over $\mathbf{R}$.

The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book.

For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Volume 83, and Geometric Analysis on Symmetric Spaces, Volume 39.

Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.

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From the Publisher:

The author was awarded "The Steele Prize" of the American Mathematical Society 1988 for this book, together with an accompanying volume, "Groups and Geometric Analysis" Academic Press, 1984

Review:

"This book has been famous for many years and used by several generations of readers. It is important that the book has again become available for a general audience." -- European Mathematical Society Newsletter

"One of the most important and excellent textbooks and a reference work about contemporary differential geometry ..." -- Zentralblatt MATH

"Important improvements in the new edition of S. Helgason's book will turn it into a desk book for many following generations." -- Mathematica Bohemica

"A great book ... a necessary item in any mathematical library." -- S. S. Chern, University of California

"Written with unmatched lucidity, systematically, carefully, beautifully." -- S. Bochner, Princeton University

"Helgason's monograph is a beautifully done piece of work and should be extremely useful for several years to come, both in teaching and in research." -- D. Spencer, Princeton University

"A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics." -- Barrett O'Neill, University of California

"Renders a great service in permitting the non-specialist, with a minimum knowledge of differential geometry and Lie groups, an initiation to the theory of symmetrical spaces." -- H. Cartan, Secretariat Mathématique, Paris

"The mathematical community has long been in need of a book on symmetric spaces. S. Helgason has admirably satisfied this need with his book, Differential Geometry and Symmetric Spaces. It is a remarkably well-written book ... a masterpiece of concise, lucid mathematical exposition ... it might be used as a textbook for "how to write mathematics"." -- Louis Auslander

"[The author] will earn the gratitude of many generations of mathematicians for this skillful, tasteful, and highly efficient presentation. It will surely become a classic." -- G. D. Mostow, Yale University

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## 1.Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)

Editorial: American Mathematical Society (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
Nuevos Tapa dura Cantidad: > 20
Librería
Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
Valoración

Descripción American Mathematical Society, 2001. Hardcover. Estado de conservación: New. Brand new. We distribute directly for the publisher. The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material.Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbf{C}$ and Cartan's classification of simple Lie algebras over $\mathbf{R}$.The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book.For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Volume 83, and Geometric Analysis on Symmetric Spaces, Volume 39.Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis. Nº de ref. de la librería 1005120066

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## 2.Differential Geometry, Lie Groups And Symmetric Spaces

ISBN 10: 0821828487 ISBN 13: 9780821828489
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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808218284890000000

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## 3.Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)

Editorial: American Mathematical Society (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
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Ergodebooks
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Descripción American Mathematical Society, 2001. Hardcover. Estado de conservación: New. Nº de ref. de la librería DADAX0821828487

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## 4.Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)

Editorial: American Mathematical Society (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
Nuevos Tapa dura Primera edición Cantidad: 1
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Irish Booksellers
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Descripción American Mathematical Society, 2001. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería 0821828487

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## 5.Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)

Editorial: American Mathematical Society (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
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Murray Media
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Descripción American Mathematical Society, 2001. Hardcover. Estado de conservación: New. Nº de ref. de la librería P110821828487

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## 6.Differential Geometry, Lie Groups, and Symmetric Spaces (Graduate Studies in Mathematics)

Editorial: Amer Mathematical Society (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
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Revaluation Books
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Descripción Amer Mathematical Society, 2001. Hardcover. Estado de conservación: Brand New. f first edition edition. 641 pages. 10.50x7.50x1.50 inches. In Stock. Nº de ref. de la librería zk0821828487

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## 7.Differential Geometry, Lie Groups and Symmetric Spaces

Editorial: American Mathematical Society (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
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Books2Anywhere
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Descripción American Mathematical Society, 2001. HRD. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería GB-9780821828489

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## 8.Differential Geometry, Lie Groups and Symmetric Spaces (Hardback)

Editorial: American Mathematical Society, United States (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
Librería
The Book Depository
(London, Reino Unido)
Valoración

Descripción American Mathematical Society, United States, 2001. Hardback. Estado de conservación: New. New edition. Language: English . Brand New Book. From reviews for the First Edition: A great book.a necessary item in any mathematical library - S. S. Chern. The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason s classic Differential Geometry, Lie Groups, and Symmetric Spaces has been - and continues to be - the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure.This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $mathbf{C}$ and Cartan s classification of simple Lie algebras over $mathbf{R}$. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book. For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS Mathematical Surveys and Monographs Series : Groups and Geometric Analysis, Volume 83 , and Geometric Analysis on Symmetric Spaces, Volume 39 . Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis. Nº de ref. de la librería AAZ9780821828489

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## 9.Differential Geometry, Lie Groups and Symmetric Spaces (Hardback)

Editorial: American Mathematical Society, United States (2001)
ISBN 10: 0821828487 ISBN 13: 9780821828489
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción American Mathematical Society, United States, 2001. Hardback. Estado de conservación: New. New edition. Language: English . Brand New Book. From reviews for the First Edition: A great book.a necessary item in any mathematical library - S. S. Chern. The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason s classic Differential Geometry, Lie Groups, and Symmetric Spaces has been - and continues to be - the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure.This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $mathbf{C}$ and Cartan s classification of simple Lie algebras over $mathbf{R}$. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book. For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS Mathematical Surveys and Monographs Series : Groups and Geometric Analysis, Volume 83 , and Geometric Analysis on Symmetric Spaces, Volume 39 . Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis. Nº de ref. de la librería AAZ9780821828489

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## 10.Differential Geometry, Lie Groups and Symmetric Spaces (Graduate Studies in Mathematics) (Hardcover)

ISBN 10: 0821828487 ISBN 13: 9780821828489
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Speedy Hen LLC
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Descripción Estado de conservación: New. Bookseller Inventory # ST0821828487. Nº de ref. de la librería ST0821828487

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