Highly curved slashing blades like the scimitar is practical for use by mounted combatants riding past one another, but the curve of the Katana is not very pronounced and the effect in cutting performance in a practical combat situation is negligible. You will loose your arm just as easily to a longsword as to a Katana. The curved blade is just a side effect of the tempering process. The hardness of the metal in different parts of the blade was controlled by the rate at which various sections were cooled during quenching. Hard steels are made by rapid quenching from high temperature, while softer steels are made to cool less quickly during quenching. To control this cooling rate, layers of clay were used. A very thin layer was painted on what would become the cutting edge, to allow the metal to cool rapidly. A much thicker layer was applied to the heavier body of the blade to slow the cooling rate creating softer, less brittle steel. If the sword survived the cooling process without breaking it ended up with the graceful curve of the Katana.
Thought not very well known, the classic curved Katana was really more common in the Sengoku and Tokugawa eras (late European Renaissance). Previously, there was a wider variety of swords. Some were straight, some not, some a little different, but all were cavalry sabers at heart. Its use as a footman's weapon was mostly confined to duels and decoration. The Samurai much preferred spears, bows, and No-Dachi for actual combat.
