Une généralisation de théorème de Myers-Steenrod aux pseudogroupes d’isométries. (A generalization of the Myers-Steenrod theorem to pseudogroups of local isometries). (French) Zbl 0613.58041

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.


58H05 Pseudogroups and differentiable groupoids
22E99 Lie groups
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