Vol. 12, No. 1, 2011

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Parallelisms of quadric sets

William Cherowitzo and Norman L. Johnson

Vol. 12 (2011), No. 1, 21–34
Abstract

In this article, it is shown that every flock of a hyperbolic quadric H and every flock of a quadratic cone C in PG(3,K), for K a field, is in a transitive parallelism of H or C, respectively. Furthermore, it is shown it is possible to have parallelisms of quadratic cones by maximal partial flocks. The theory of parallelisms of quadratic cones is generalized to analogous results for parallelisms of α-cones.

Keywords
flocks, flokki, parallelisms, hyperbolic quadric, elliptic quadric, quadratic cone, $\alpha$-cone
Mathematical Subject Classification 2010
Primary: 51A15, 51E20
Milestones
Received: 31 August 2009
Accepted: 25 September 2009
Authors
William Cherowitzo
University of Colorado at Denver
CO
United States
Norman L. Johnson
University of Iowa
IA
United States