Lie Groups and Geometric Aspects of Isometric Actions

Authors: Alexandrino, Marcos M., Bettiol, Renato G.

  • 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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eBook 71,39 €
price for Spain (gross)
  • ISBN 978-3-319-16613-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-16612-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-38627-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.

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.

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)


Table of contents (6 chapters)

  • Basic Results on Lie Groups

    Alexandrino, Marcos M. (et al.)

    Pages 3-25

    Preview Buy Chapter 30,19 €
  • Lie Groups with Bi-invariant Metrics

    Alexandrino, Marcos M. (et al.)

    Pages 27-47

    Preview Buy Chapter 30,19 €
  • Proper and Isometric Actions

    Alexandrino, Marcos M. (et al.)

    Pages 51-84

    Preview Buy Chapter 30,19 €
  • Adjoint and Conjugation Actions

    Alexandrino, Marcos M. (et al.)

    Pages 85-107

    Preview Buy Chapter 30,19 €
  • Polar Foliations

    Alexandrino, Marcos M. (et al.)

    Pages 109-137

    Preview Buy Chapter 30,19 €

Buy this book

eBook 71,39 €
price for Spain (gross)
  • ISBN 978-3-319-16613-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-16612-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-319-38627-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Lie Groups and Geometric Aspects of Isometric Actions
Authors
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-16613-1
DOI
10.1007/978-3-319-16613-1
Hardcover ISBN
978-3-319-16612-4
Softcover ISBN
978-3-319-38627-0
Edition Number
1
Number of Pages
X, 213
Number of Illustrations and Tables
14 b/w illustrations
Topics