Cherowitzo, William E.; Johnson, Norman L. Parallelisms of quadric sets. (English) Zbl 1305.51007 Innov. Incidence Geom. 12, 21-34 (2011). For a field \(K\), and a flock of a quadratic cone, an elliptic quadric or a hyperbolic quadric in \(PG(3,K)\), a parallelism refers to a set of mutually disjoint flocks, whose union is a complete cover of the set of conics of plane intersections of the quadric. The authors show that every flock of a hyperbolic quadric \(H\) and every flock of a quadratic cone \(C\) in \(PG(3,K)\) is in a transitive parallelism of \(H\) or \(C\) respectively. Additionally, it is shown that it is possible to have parallelisms of quadratic cones by maximal partial flocks. Parallelisms by \(\alpha\)-flokki of \(\alpha\)-cones, which are a generalization of quadratic cones, are also considered. The authors end by stating four open problems concerning parallelisms. Reviewer: Steven T. Dougherty (Scranton) Cited in 1 Document MSC: 51E20 Combinatorial structures in finite projective spaces 51A15 Linear incidence geometric structures with parallelism Keywords:flocks; flokki; parallelisms; hyperbolic quadric; elliptic quadric; quadratic cone; \(\alpha\)-cone PDFBibTeX XMLCite \textit{W. E. Cherowitzo} and \textit{N. L. Johnson}, Innov. Incidence Geom. 12, 21--34 (2011; Zbl 1305.51007)