Abstract: In a pipe connection having a cutting ring comprising a metallic compound, in particular an alloy with the constituents CrNiMo, which cutting ring surrounds the pipe wall and can be pressed into same with at least one cutting edge, the cutting ring is cut to length and shaped from an elongate portion, in particular a hollow profile member or tube, that is drawn from stainless steel and cold hardened. A cutting ring (16) according to the invention of that kind is preferably cut to length from a tube drawn from stainless steel, and then shaped and cold hardened.