Lie Groups and Geometric Aspects of Isometric Actions

“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)