Lie Groups and Geometric Aspects of Isometric Actions

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.

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.