Geodesic
On the twisted cubic of ${PG}(3, q)$
Journal of Algebraic Combinatorics, Tome 18 (2003) no. 3, pp. 255-262.

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Summary: In this paper we classify the lines of $P$G$(3, q)$ whose points belong to imaginary chords of the twisted cubic of $P$G$(3, q)$. Relying on this classification result, we obtain a complete classification of semiclassical spreads of the generalized hexagon $H( q)$.
Keywords: twisted cubics, generalized hexagons, coset geometries, spreads 
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     title = {On the twisted cubic of ${PG}(3, q)$},
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Lunardon, G.; Polverino, O. On the twisted cubic of ${PG}(3, q)$. Journal of Algebraic Combinatorics, Tome 18 (2003) no. 3, pp. 255-262. http://geodesic.mathdoc.fr/item/JAC_2003__18_3_a0/