don't remember where or who .. but i think it was from a martial arts instructor. anyways I have no idea if there is any truth to this for sure so consider it food for thought.
The curve in the sword is so that more force is applied to a smaller area making it easyer to cut an object, be it a tree, an arm, or someoen head. One draw, one swing, one kill.
in my eyes this makes sence in addition to the physics of the forging process that a smaller edge with X ammount of force behind it would apply more force on an object being struck then a larger edge (ie flat blade) with the same X ammount of force behind it. ie it is easyer to stab somone with a nail then it is with a blunt 2x4 given that you stab with the same ammount of force. There is just more poundes per square inch applied to the object being struck with a curved blade.
well that is my contribution, maybe someone "in the know" can fill in and give the tumbs up or down on this info *shrugs*.