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Sep 28, 2012 at 15:41 comment added paul garrett Sure, we know in advane that there is a Riemannian metric... the above is not quite it, but has tha elementary description if one wants.
Sep 28, 2012 at 11:12 comment added Deane Yang Theo, many thanks for the correction.
Sep 28, 2012 at 3:19 comment added Theo Johnson-Freyd @Deane, for the question of distance functions, probably you have to be careful when your group has $\pi_0$. But your general point is correct.
Sep 28, 2012 at 2:35 comment added Deane Yang I'm lost here. Doesn't any Lie group have a left invariant Riemannian metric and therefore a left invariant "ordinary metric"?
Sep 27, 2012 at 21:17 history answered paul garrett CC BY-SA 3.0