This publication presents easy access to the speculation of Lie teams and isometric activities on tender manifolds, utilizing a concise geometric strategy. After a gradual creation to the topic, a few of its contemporary purposes to lively examine parts are explored, preserving a continuing reference to the elemental fabric. the themes mentioned comprise polar activities, singular Riemannian foliations, cohomogeneity one activities, and definitely curved manifolds with many symmetries. This booklet stems from the adventure accrued through the authors in different lectures alongside the years and was once designed to be as self-contained as attainable. it really is meant for complicated undergraduates, graduate scholars and younger researchers in geometry and will be used for a one-semester direction or autonomous research.
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