Smooth Actions of Lie Groups
In many areas of mathematics, Lie groups appear naturally as symmetry groups. Examples are groups of isometries of Riemannian manifolds, groups of holomorphic automorphisms of complex domains, or groups of canonical transformations in hamiltonian mechanics. In all these cases, one considers group actions on manifolds by smooth maps. Even though the focus of this book is the geometry and structure theory of Lie groups rather than their applications, we have to study the concept of a smooth action of a Lie group on a manifold in some detail since it is an essential tool in the smooth versions of group theoretic considerations like the study of quotient groups and conjugacy classes.
KeywordsVector Field Vector Bundle Homogeneous Space Tensor Field Manifold Structure
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