Innovations in Incidence Geometry

Parallelisms of quadric sets

William E. Cherowitzo and Norman L. Johnson

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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.

Article information

Innov. Incidence Geom., Volume 12, Number 1 (2011), 21-34.

Received: 31 August 2009
Accepted: 25 September 2009
First available in Project Euclid: 28 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51A15: Structures with parallelism 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx]

flocks flokki parallelisms hyperbolic quadric elliptic quadric quadratic cone $\alpha$-cone


Cherowitzo, William E.; Johnson, Norman L. Parallelisms of quadric sets. Innov. Incidence Geom. 12 (2011), no. 1, 21--34. doi:10.2140/iig.2011.12.21.

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