Une généralisation de théorème de Myers-Steenrod aux pseudogroupes d'isométries. (A generalization of the Myers-Steenrod theorem to pseudogroups of local isometries) (Q1819453)

We show that every pseudogroup of local isometries on a Riemannian manifold, which is complete and closed for the \(C^ 1\)-topology is a Lie pseudogroup. This result is a generalization of the well-known theorem of S. Myers and N. Steenrod according to which the group of isometries of a Riemann manifold is a Lie group.