In the explanation of Lines of Partition by none other than J.P.Brook-Little, he states that in British heraldry a single curve and a double curve are actually partition lines with the names of "Arched or enarched or archy" for the single curve and "Double arched, enarched or archy" for the double curve. The tri-curve is not mentioned in British heraldry and I have yet to see one in that heraldic jurisdiction. I believe that the nearest you would get to the tri-arched line might be found somewhere in Scottish or Irish heraldry.
Rgds,