Characterising hyperbolic hyperplanes of a non-singular quadric in $PG(4,q)$

Abstract

Let $H$ be a non-empty set of hyperplanes in $PG(4,q)$, $q$ even, such that every point of $PG(4,q)$ lies in either $0$, $\frac{1}{2}{q}^3$ or $\frac{1}{2}(q^3+q^2)$ hyperplanes of $H$, and every plane of $PG(4,q)$ lies in $0$ or at least $\frac{1}{2}q$ hyperplanes of $H$. Then $H$ is the set of all hyperplanes which meet a given non-singular quadric $Q(4,q)$ in a hyperbolic quadric.

arXiv admin note: text overlap with arXiv:1906.03985