We propose a definition of a Riemannian groupoid, and we show that the Stefan foliation that it induces is a Riemannian (singular) foliation. We also prove that the homotopy groupoid of a Riemannian (regular) foliation is a Riemannian groupoid.
@article{urn:eudml:doc:41080, title = {Groupo\"\i des riemanniens.}, journal = {Publicacions Matem\`atiques}, volume = {33}, year = {1989}, pages = {417-422}, mrnumber = {MR1038480}, zbl = {0704.53024}, language = {fr}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41080} }
Gallego, E.; Gualandri, L.; Héctor, G.; Reventós, A. Groupoïdes riemanniens.. Publicacions Matemàtiques, Tome 33 (1989) pp. 417-422. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41080/