I am currently studying a French paper on Einstein manifolds by Berard Bergery and I have doubts that my translation of the following sentence is correct:
De plus, puisque $G$ agit par isometries, $M/G$ herite par quotient d'une metrique, qui est enfait une metrique riemannienne ("a bord" eventuellement).
Furthermore, since $G$ acts by isometries, the quotient $M/G$ inherits a metric, which is actually a Riemannian metric (possibly (..)).
Is this correct so far? I don't know how to translate the last two words, apologies for leaving out the accents!