Translating French paper into English

Question

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).

My translation:

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!

Answer 1

Furthermore, since $G$ acts by isometries, $M/G$ inherits by the quotient operation a metric, which is in fact a Riemannian metric (possibly with boundary).

Probably the last part means "the metric of a Riemannian manifold, possibly with boundary", but the French is not quite saying that.

Note that "enfait" should have been "en fait".

Answer 2

Good except "$M/G$ hérite par quotient d'une métrique" actually means "$M/G$ inherits a metric by quotient".

"à bord eventuellement" means "possibly on the edge" but not sure of the context.

I guess you got the meaning right.