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.
Quadratic sets of a 3-dimensional locally projective regular planar space--
DI GENNARO, Roberta;
2004-01-01
Abstract
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.File in questo prodotto:
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