IIRC the Japanese picked up the curvy sabre from the Continent around the same time they imported horse riding, ie. around something like 9th cent AD. Would make sense for the two to come together anyway, what with sabres having developed as cavalry weapons to begin with. (IIRC it was also the "northern barbarians" the Yamato were slowly absorbing who first took to both with gusto.) The thing was called tachi back then though; there's some functional difference between those and the later katanas (though, both were made and used in like zillion different varieties like all swords), but I can't be arsed to look up the details ATM.
Anyways, the big three Japanese weapons were the bow, the spear and the glaive (ie. naginata); the sword was only ever a backup on the battlefield, though obviously a lot more relevant as a "civilian carry" sidearm for all the usual reasons. AFAIK if you had to try to kill a guy in decent armour with it (and the Japanese made their lamellar out of iron and hide like everyone else kthx; the laquering was for decoration and rust-proofing, Japan having a rather tropical climate in parts) you went for the relatively large gaps at the joints and around the throat, as sabre slashes kinda suck against armour by what I know of it.
Anyways, as for the Vikings, weren't their swords kinda light compared to the later Medieval types in the usual "Dark Ages" fashion ? I always figured the relative scarcity of metal armour at the time had a lot to do with that, plus if you had to whack a guy in mail axes were a lot better for it and quite ubiquitous - every household had at least one as an everyday tool after all, and such can pull decent duty as a weapon as needed.
Also, from what I gather trial-by-combat (ie. judicial duels) were a pretty common means of solving disputes; Holmgånga, anyone ? Between that and the usual smattering of less formal interpesonal dispute-setting the old-fashioned way, I daresay the Vikings were by and large pretty adept at one-on-one fights...
Regarding iron in Scandinavia, bog iron AFAIK used to be quite common indeed in at least Sweden and Finland (where it was still being gathered in late 1800s, though that region didn't partake overmuch in the better-known "Viking Age" stuff - the Finns seem to have restricted their activities to the Baltic), which both also have copious amounts of forest to provide the necessary fuel. I understand bog iron is kinda crappy quality-wise though, but at least it was common and comparatively easy to get hence relatively cheap. I'd imagine most smiths wouldn't have been able to make anything too impressive out of the stuff - inclusing at least the longer swords, whose blades AFAIK were for the most part imported from the more advanced parts of Europe. I know French monarchs on several occasions (which speaks volumes of the degree to which the edicts were respected) outlawed the sale of quality sword blades to the Scandinavians, and quite a few sword finds from the period bear the "trademark" inscription of one of the major German manufacturies of the period - INGELRII, CIGELIN and in particular that industry giant, ULFBERTH...
As for mail, AFAIK the big problem with that stuff was the sheer amount of labour even a simple byrnie demands and the resultant high price tag and minor problems in organising the manufacturing chain. And Scandinavia being comparatively piss-poor by European standards and at the time rather lacking the kind of infrastructure needed to support such operations in any larger scale, hence such protection being quite costly relative to the wealth level and only normally found among the more prosperous warriors (and lucky looters...). Well, that's what shields are for anyway.
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