## 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.

### MSC:

 58H05 Pseudogroups and differentiable groupoids 22E99 Lie groups

### Keywords:

pseudogroups of local isometries; Lie pseudogroups
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### References:

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