For rimfire and centerfire a fluted barrel provides a weight advantage for a given barrel diameter with the claim that it doesn't effect the rigidity of the barrel. In a center fire, it dissipates heat faster due to the increased surface area, and less mass. There is no effect on accuracy if the barrel is properly fluted. Whether these effects are noticeable enough to make an "observed" difference may be debatable. I have both rimfire and centerfire with both standard and fluted barrels. I can take them or leave them depending on the esthetics or availability of a given rifle.
YEP.. I will add that Krieger (I THINK) states on their site that a fluted barrel is actually more ridged than a non fluted barrel of the same contour..I think I have that right..I should go try to find that but I am too lazy
This is close, but you remembered incorrectly. Removing material does not make something more rigid. However, flutes will allow a barrel to be more rigid than a non fluted barrel of the same weight, but the non fluted barrel has to be a smaller contour to weigh the same.
Read this link for more info:
Fluting
So just shooting from the hip, how much weight would you think is saved by fluting something like a #5 or #6, 26" barrel?