Quadratic sets of a 3-dimensional locally projective regular planar space--

In this paper quadratic sets of a 3-dimensional locally projective regular planar space (S,L,P) of order n are studied and classified. It is proved that if in (S,L,P) there is a non-degenerate quadratic set H, then the planar space is either PG(3, n) or AG(3, n). Moreover in the first case H is either an ovoid or an hyperbolic quadric, in the latter case H is either a cylinder with base an oval or a pair of parallel planes.