Often shotguns will be advertised with Vent Rib (VR) barrels. The Vent Rib is a flat piece of metal that is set along the length of the top of the barrel, extended from just in front of the receiver to the muzzle. This rib is usually vented, in that it is not is constant contact with the barrel, looking at it from the side, it looks like a bridge, with pillars coming down to make contact with the barrel every 1/2-1" or so. This 'venting' is intended to prevent the thermal expansion of the barrel from breaking the rib loose, as well as minimizing the heat transfer from the barrel to the rib.
The function of the rib is to provide a smooth sighting plane for the eye to follow along when aiming the shotgun, as well as to minimize the mirage in the sighting plane produced by barrel heat.