6
$\begingroup$

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!

$\endgroup$
  • 2
    $\begingroup$ "Une variété à bord" translates as "a manifold with boundary", so here we might have "a riemannian metric, possibly with boundary". But I don't know if such a concept exists (the standard books on differential manifolds don't seem to cover riemannian metrics on manifolds with boundary) $\endgroup$ – Georges Elencwajg Sep 10 '13 at 14:17
  • $\begingroup$ "À bord" is "with boundary". Ref. $\endgroup$ – Did Sep 10 '13 at 14:19
  • $\begingroup$ @Did: les bons esprits se rencontrent :-) $\endgroup$ – Georges Elencwajg Sep 10 '13 at 14:20
  • $\begingroup$ @GeorgesElencwajg En vérité. Mais votre commentaire (que je n'avais pas vu en tapant le mien) est plus complet. $\endgroup$ – Did Sep 10 '13 at 14:22
  • $\begingroup$ @GeorgesElencwajg this is what confused me, too (i.e. a Riemannian metric with boundary). $\endgroup$ – harlekin Sep 10 '13 at 14:23
4
$\begingroup$

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".

$\endgroup$
  • $\begingroup$ Yes, indeed that should have been "en fait" (I'll leave it as it is so as to not interfere indirectly with your answer). Many thanks! $\endgroup$ – harlekin Sep 10 '13 at 14:25
0
$\begingroup$

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.

$\endgroup$
  • 2
    $\begingroup$ "On the edge": no. $\endgroup$ – Did Sep 10 '13 at 14:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.