Overview
Includes an elementary introduction to Lie groups and Lie algebras
Uses a geometric approach that renders the text simultaneously complete and considerably short
Discusses recent topics on isometric actions, cohomogeneity one actions and positive curvatures and singular Riemannian foliations
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Table of contents (6 chapters)
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Front Matter
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Lie Groups
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Front Matter
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Isometric Actions
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Front Matter
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Back Matter
Keywords
About this book
Reviews
“This book sets out from the geometric point of view the foundations of the theory of Lie groups and Lie algebras, as well as some of the topics relating to the theory of Lie groups of isometric transformations. … At the end of the book there is an application in which some elements of the theory of smooth manifolds are exposed. The book therefore can be seen as self-contained and thus usable as a textbook.” (Vladimir V. Gorbatsevich, Mathematical Reviews, March, 2016)
“The present book provides a nice overview of topics related to isometric actions, exploring relations to active research areas (primarily of the authors), such as isoparametric submanifolds, polar actions, polar foliations, cohomogeneity one actions, and positive curvature via symmetries. … The book is of great benefit for mature graduate students or researchers in the field.” (Andreas Arvanitoyeorgos, zbMATH 1322.22001, 2015)
Authors and Affiliations
About the authors
Marcos M. Alexandrino is an Associate Professor at the Institute of Mathematics and Statistics of the University of São Paulo, Brazil. He did his PhD at Pontifical Catholic University of Rio de Janeiro, Brazil, with studies at the University of Cologne, in Germany. His research is on the field of Differential Geometry, more specifically on singular Riemannian foliations and isometric actions.
Renato G. Bettiol is a Hans Rademacher Instructor of Mathematics at the University of Pennsylvania, USA. He did his PhD at the University of Notre Dame, USA. His research is on the field of Differential Geometry, more specifically on Riemannian geometry and geometric analysis.
Bibliographic Information
Book Title: Lie Groups and Geometric Aspects of Isometric Actions
Authors: Marcos M. Alexandrino, Renato G. Bettiol
DOI: https://doi.org/10.1007/978-3-319-16613-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-16612-4Published: 09 June 2015
Softcover ISBN: 978-3-319-38627-0Published: 17 October 2016
eBook ISBN: 978-3-319-16613-1Published: 22 May 2015
Edition Number: 1
Number of Pages: X, 213
Number of Illustrations: 14 b/w illustrations
Topics: Differential Geometry, Topological Groups, Lie Groups, Algebraic Topology