Lie Groups and Geometric Aspects of Isometric Actions

  • Marcos M. Alexandrino
  • Renato G. Bettiol

Table of contents

  1. Front Matter
    Pages i-x
  2. Lie Groups

    1. Front Matter
      Pages 1-1
    2. Marcos M. Alexandrino, Renato G. Bettiol
      Pages 3-25
    3. Marcos M. Alexandrino, Renato G. Bettiol
      Pages 27-47
  3. Isometric Actions

    1. Front Matter
      Pages 49-49
    2. Marcos M. Alexandrino, Renato G. Bettiol
      Pages 51-84
    3. Marcos M. Alexandrino, Renato G. Bettiol
      Pages 85-107
    4. Marcos M. Alexandrino, Renato G. Bettiol
      Pages 109-137
    5. Marcos M. Alexandrino, Renato G. Bettiol
      Pages 139-183
  4. Back Matter
    Pages 185-213

About this book

Introduction

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.

Keywords

Cheeger deformation Frobenius theorem Lie algebras Lie groups Riemannian geometry Weyl group cohomogeneity one action isometric actions maximal tori polar actions positive curvature proper actions

Authors and affiliations

  • Marcos M. Alexandrino
    • 1
  • Renato G. Bettiol
    • 2
  1. 1.Departamento de MatemáticaInstituto de Matemática e Estatística, Universidade de São PauloSão PauloBrazil
  2. 2.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-16613-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16612-4
  • Online ISBN 978-3-319-16613-1
  • About this book
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