Differential Geometry Lie Groups And Symmetric Spaces
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Differential Geometry Lie Groups And Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: Academic Press
Release Date : 1979-02-09
Differential Geometry Lie Groups And Symmetric Spaces written by Sigurdur Helgason and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-02-09 with Mathematics categories.
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.
Differential Geometry Lie Groups And Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-06-12
Differential Geometry Lie Groups And Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-12 with Mathematics categories.
A great book ... a necessary item in any mathematical library. --S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. --Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. --Andre Weil, Institute for Advanced Study 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. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. 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 $\mathbb{C}$ and Cartan's classification of simple Lie algebras over $\mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.
Groups And Geometric Analysis
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-17
Groups And Geometric Analysis written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-17 with Mathematics categories.
Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.
Differential Geometry And Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-01-16
Differential Geometry And Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-16 with Mathematics categories.
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.
Semisimple Groups And Riemannian Symmetric Spaces
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Author : Armand Borel
language : en
Publisher: Springer
Release Date : 1998-12-15
Semisimple Groups And Riemannian Symmetric Spaces written by Armand Borel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-15 with Mathematics categories.
Differential Geometry And Lie Groups
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Author : Jean Gallier
language : en
Publisher: Springer Nature
Release Date : 2020-08-18
Differential Geometry And Lie Groups written by Jean Gallier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-18 with Mathematics categories.
This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Differential Geometry Lie Groups And Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-19
Differential Geometry Lie Groups And Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-19 with Mathematics categories.
A great book … a necessary item in any mathematical library. —S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. —Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. —André Weil, Institute for Advanced Study 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. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. 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 $mathbb{C}$ and Cartan's classification of simple Lie algebras over $mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.
Lectures On Lie Groups
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Author : J. F. Adams
language : en
Publisher: University of Chicago Press
Release Date : 1982
Lectures On Lie Groups written by J. F. Adams and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
"[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky
Differential Geometry Lie Groups And Symmetric Spaces
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Author : SIGURDUR. HELGASON
language : en
Publisher:
Release Date : 2012
Differential Geometry Lie Groups And Symmetric Spaces written by SIGURDUR. HELGASON and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.