# Group acting by Isometries

• Jul 20th 2011, 02:35 AM
cavey
Group acting by Isometries
Hey guys, quick question. What is the definition of a group acting by isometries on a metric space?

Thanks.
• Jul 20th 2011, 05:51 AM
Swlabr
Re: Group acting by Isometries
Quote:

Originally Posted by cavey
Hey guys, quick question. What is the definition of a group acting by isometries on a metric space?

Thanks.

Is it not simply that the group action is an isometry? As in, writing $x^g$ for the action of $g$ on $x\in X$ you have that,

$d(x^g, y^g)=d(x, y)$.
• Jul 20th 2011, 10:28 AM
cavey
Re: Group acting by Isometries
Thanks for the help.