I used to ski all the time. I hiked up ridges and fell down chutes and clawed my way out of tree wells. I had what were probably first generation parabolic skis. These are not pictures of my skis. These are pictures of skis which were designed and built (yep, there are some working prototypes out there) by Charlie Pyott.
The theory, one must assume, is that the more edges you have in contact with the snow, the more maneuverability and control you will have. The skis themselves look as if they are a couple of x-country skis with a hinge holding them together and a third floating element that sits on top of the actual skis and houses the bindings. No data is available on the actual ride, presumably because they have yet to be ridden or are, in fact, very dangerous.
I am seeing some things right off the bat that would scare the crap out of me if I were not on nice well-groomed runs. First and foremost, I want to know what happens if that front hinge gives out. Will the ski just disintegrate? Can you ditch half your ski? But what would the binding then attach to? Blah...prototype is right.
