The proper term would be "fuller" - it ain't got a jack to do with the other guy's blood, but rather serves to lighten the blade and tweak its balance characteristics without compromising structural integrity.
That said, I'm under the vague impression the weaponsmiths hadn't yet figured it out during (most of) the EB timeframe, and just made their blades either smoothly lenticular or *very* flat rhomboid in profile (or seriously flattened hexagon, but you get the idea). Not sure how reliably accurate
this is, but it's what I could scrounge up quickly.
Late Imperial period swords did apparently start featuring fullers, tho'. I've gotten the impression the "barbarians" generally preferred a single wide one, whereas Roman designs tended to go for multiple narrow ones. But, then again, that was also the period when even the humble infantry sword had started growing quite a bit in lenght...
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