LAUSR

We identify various structures on the configuration space C of a flying saucer, moving in a three-dimensional smooth manifold  M . Always C is a five-dimensional contact manifold. If M has a projective structure, then C is its twistor space and is equipped with an almost contact Legendrean structure. Instead, if M has a conformal structure, then the saucer moves according to a CR structure on  C . With yet another structure on M , the contact distribution in C is equipped with a cone over a twisted cubic. This defines a certain type of Cartan geometry on  C (more specifically, a type of ‘parabolic geometry’) and we provide examples when this geometry is ‘flat,’ meaning that its symmetries comprise the split form of the exceptional Lie algebra  $${\mathfrak {g}}_2$$ g 2 .