AUTOMORPHISM GROUPS

In these lecture notes I discuss groups of automorphisms of certain natural structures which occur in differential geometry. My aim is to show that such groups of automorphisms, when endowed with the compact–open topology, are Lie transformation groups. Many of the automorphism groups from differential geometry can be viewed as closed subgroups of automorphism groups of parallelizations. For example, this is the case for the group of isometries of a Riemannian or pseudo-Riemannian manifold, see Example 3.2. In the first part of these notes I therefore treat the case of parallelized manifolds. I would like to thank Dorothee Schüth for helpful criticism. More criticism is welcome.