Pseudogroups of local isometries. (English) Zbl 0656.58042

Differential geometry, Proc. 5th Int. Colloq., Santiago de Compostela/Spain 1984, Res. Notes Math. 131, 174-197 (1985).
[For the entire collection see Zbl 0637.00004.]
The paper starts with a nice survey of the contemporary theory of pseudogroups and foliations. Then the author presents the generalized bundle theory for the pseudogroup case. After that the notion of complete pseudogroups of isometries is introduced, which is a natural generalization of holonomy pseudogroups of complete Riemannian foliations. Such an approach enables the author to deduce several classification results of different types.
Reviewer: I.Kolář


58H05 Pseudogroups and differentiable groupoids
57R30 Foliations in differential topology; geometric theory


Zbl 0637.00004