Flexible Fluid-Lubricated Foils, or better known as Magic Carpets

This is what Physics researchers do for fun and fantasy -)

New Scientist  on the physics of flying carpets "a 10cm long carpet 0.1 millimetres thick would have to vibrate with 0.25 millimetre high waves 10 times a second to stay aloft in air and fly horizontally at 0.3 metres per second."