Twisted hyperbolic flocks

We give a generalization of the theory of flocks of hyperbolic quadrics in PG $(3, q)$ to what is called an $α$ -twisted hyperbolic flock in an arbitrary $3$ -dimensional projective space over a field $K$ . We obtain an equivalence between a set of translation planes with spreads in PG $(3, K)$ that admit affine homology groups such that the axis and coaxis and one orbit is a twisted regulus. Examples and generalizations are also given.

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Keywords

hyperbolic flock, twisted hyperbolic flock, derivable net-inducing groups

Mathematical Subject Classification

Primary: 51E20

Secondary: 51E14

Milestones

Received: 13 September 2020

Revised: 15 January 2021

Accepted: 14 March 2021

Published: 17 April 2021

Authors

Norman L. Johnson
Mathematics Department University of Iowa Iowa City, IA 52245 United States

Vol. 19, No. 1, 2021-2022

Norman L. Johnson

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors