Aerodynamics of flying saucers (Q2181971)

The authors identify various structures on the configuration space $C$ of a flying saucer, moving in a three-dimensional smooth manifold $ M$. When $M$ has a projective structure, an almost contact Legendrean structure on $C$ is found and it is shown that $M$ is projectively flat if and only if $C$ has maximal symmetry $\mathfrak{sl}(4,\mathbb{R})$. If $M$ has a conformal structure, then it is shown that the saucer moves according to a CR structure on $C$. Some nice examples are also given.