Quadratic sets of a $3$-dimensional locally projective regular planar space
Di Gennaro, Roberta ; Durante, Nicola
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, p. 281-288 / Harvested from Project Euclid
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In this paper quadratic sets of a $3$-dimensional locally projective regular planar space $(\cal S,\cal L,\cal P)$ of order $n$ are studied and classified. It is proved that if in $(\cal S,\cal L,\cal P)$ there is a non-degenerate quadratic set $\bf H$, then the planar space is either $\mathop{\rm{PG}}(3,n)$ or $\mathop{\rm{AG}}(3,n)$. Moreover in the first case $\bf H$ is either an ovoid or an hyperbolic quadric, in the latter case $\bf H$ is either a cylinder with base an oval or a pair of parallel planes.
Publié le : 2004-06-14
Classification:  
@article{1086969318,
     author = {Di Gennaro, Roberta and Durante, Nicola},
     title = {Quadratic sets of a $3$-dimensional locally projective regular
planar space},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {1},
     year = {2004},
     pages = { 281-288},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1086969318}
}

Di Gennaro, Roberta; Durante, Nicola. Quadratic sets of a $3$-dimensional locally projective regular
planar space. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp.  281-288. http://gdmltest.u-ga.fr/item/1086969318/