Cayley's surface revisited (Q2573760)

Cayley's (ruled cubic) surface carries a three-parameter family of twisted cubics. Here a complete description of their order of contact is given. In particular, it is shown that there are infinitely many one-parameter families of twisted cubics with contact of order four. The existence of such a family was doubted by \textit{H. Brauner} [Geometrie auf der Cayleyschen Fläche, Österr. Akad. Wiss., Math.-Naturw. Kl., S.-Ber., Abt. II 173, 93--128 (1964; Zbl 0134.17402)]. The dual contact is also investigated, and relations to isotropic geometry are exhibited.