Vol. 19, No. 1, 2021-2022

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Twisted hyperbolic flocks

Norman L. Johnson

Vol. 19 (2021-2022), No. 1, 1–23

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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hyperbolic flock, twisted hyperbolic flock, derivable net-inducing groups
Mathematical Subject Classification
Primary: 51E20
Secondary: 51E14
Received: 13 September 2020
Revised: 15 January 2021
Accepted: 14 March 2021
Published: 17 April 2021
Norman L. Johnson
Mathematics Department
University of Iowa
Iowa City, IA 52245
United States