The "curve" on the blade increases the torque transmitted to the tip of the sword compared to the straight blades. While considering a swing maneuver ( imagine a from-right-to-left swing) , curved blade satisfies a longer continious arc of cutting edge. This can also be explained as a longer "time" of cutting, as while the blade follows the trajectory of the swing, arc still penetrates the target because of the circular shape. Combining these two properties, 1) higter torque on tip of blade 2) longer penetration interval, you have a very effective cutting sword.
As the western unit types are favored by full plate or mails, eastern units preferred these curved blades to increase their chances in inflicting more damage agains these armors. As the weakest spots on these armors are the body joint locations, such as gap between helmet and neck cover, arm and armpit gaps, knee cover gaps ... such curved blades were effectively used on these points. This might be the reason why some friends here insist on armor bonus points.
When we talk about "recurve" as in yataghan, this modification still kept the previous skills of curved blades, but also increasing the durability of the blade. I also remember reading in a journal that those recurved blades were very effective for beheading

I'm not sure whether this satisfies your scientific needs but if you are really interested in learning the details, I suggest you to open and read some militaristic books ;)