In this article, the lines not meeting a hyperbolic quadric in PG\((3,q)\) are characterized by their intersection properties with points and planes.
Citation
Stefano Innamorati, Mauro Zannetti, Fulvio Zuanni. A Characterization of the Lines External to a Hyperbolic Quadric in PG\((3, 4)\)[J], Ars Combinatoria, Volume 103. 3-11. .