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Differential Geometry Lie Groups And Symmetric Spaces
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Book Synopsis Differential Geometry, Lie Groups, and Symmetric Spaces by : Sigurdur Helgason
Download or read book Differential Geometry, Lie Groups, and Symmetric Spaces written by Sigurdur Helgason and published by Academic Press. This book was released on 1979-02-09 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential Geometry and Symmetric Spaces by :
Download or read book Differential Geometry and Symmetric Spaces written by and published by Academic Press. This book was released on 1962-01-01 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry and Symmetric Spaces
Book Synopsis Lie Groups, Physics, and Geometry by : Robert Gilmore
Download or read book Lie Groups, Physics, and Geometry written by Robert Gilmore and published by Cambridge University Press. This book was released on 2008-01-17 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
Book Synopsis Groups and Geometric Analysis by : Sigurdur Helgason
Download or read book Groups and Geometric Analysis written by Sigurdur Helgason and published by American Mathematical Society. This book was released on 2022-03-17 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Lie Groups and the Geometry of Homogeneous Spaces by : Andreas Arvanitogeōrgos
Download or read book An Introduction to Lie Groups and the Geometry of Homogeneous Spaces written by Andreas Arvanitogeōrgos and published by American Mathematical Soc.. This book was released on 2003 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.
Book Synopsis Differential Geometry and Lie Groups by : Jean Gallier
Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer Nature. This book was released on 2020-08-14 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.
Book Synopsis Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings by : Wolfgang Bertram
Download or read book Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings written by Wolfgang Bertram and published by American Mathematical Soc.. This book was released on 2008 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.
Book Synopsis Differential Geometry and Lie Groups by : Jean Gallier
Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer Nature. This book was released on 2020-08-18 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spaces of Constant Curvature by : Joseph Albert Wolf
Download or read book Spaces of Constant Curvature written by Joseph Albert Wolf and published by . This book was released on 1974 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry and Symmetric Spaces by : Sigurdur Helgason
Download or read book Differential Geometry and Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Society. This book was released on 2024-04-05 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Causal Symmetric Spaces by : Gestur Olafsson
Download or read book Causal Symmetric Spaces written by Gestur Olafsson and published by Academic Press. This book was released on 1996-09-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces. Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spaces Deals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fields Presents basic geometric properties of semi-simple symmetric spaces Includes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
Book Synopsis Differential Geometric Structures by : Walter A. Poor
Download or read book Differential Geometric Structures written by Walter A. Poor and published by Courier Corporation. This book was released on 2015-04-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Book Synopsis Lie Theory and Geometry by : Jean-Luc Brylinski
Download or read book Lie Theory and Geometry written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant’s fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant’s work.
Book Synopsis Lectures on Lie Groups by : J. F. Adams
Download or read book Lectures on Lie Groups written by J. F. Adams and published by University of Chicago Press. This book was released on 1982 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: "[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
Book Synopsis Offbeat Integral Geometry on Symmetric Spaces by : Valery V. Volchkov
Download or read book Offbeat Integral Geometry on Symmetric Spaces written by Valery V. Volchkov and published by Springer Science & Business Media. This book was released on 2013-01-30 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.
Book Synopsis A Course in Differential Geometry and Lie Groups by : S. Kumaresan
Download or read book A Course in Differential Geometry and Lie Groups written by S. Kumaresan and published by Springer. This book was released on 2002-01-15 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
