A characterization of the planes meeting a hyperbolic quadric of $\PG(3,q)$ in a conic

TL;DR

This paper provides a combinatorial characterization of planes in projective 3-space that intersect a hyperbolic quadric in a conic, based on their intersection properties with points and lines.

Contribution

It introduces a novel combinatorial approach to identify planes meeting a hyperbolic quadric in an irreducible conic within PG(3,q).

Findings

Characterization of planes intersecting a hyperbolic quadric in a conic

Use of intersection properties with points and lines for identification

Provides a new combinatorial framework for geometric configurations

Abstract

In this article, a combinatorial characterization of the family of planes of $\PG(3,q)$ which meet a hyperbolic quadric in an irreducible conic, using their intersection properties with the points and lines of $\PG(3,q)$, is given.