Dimensional dual hyperovals in classical polar spaces (Q310252)

\textit{S. Yoshiara} [in: Finite geometries, groups, and computation. Proceedings of the conference, Pingree Park, CO, USA, September 4--9, 2004. Berlin: Walter de Gruyter. 247--266 (2006; Zbl 1100.51006), Problem 4.7] asked: Does the existence of an \(n\)-dimensional dual hyperoval in a polar space imply that \(n\) is odd? Applying a theorem of \textit{F. Vanhove} [J. Comb. Des. 19, No. 3, 202--216 (2011; Zbl 1226.05076)] the author shows the following theorem: Suppose \(\mathcal D\) is an \(n\)-dimensional dual hyperoval in a polar space \(\mathcal P\) of rank \(n\). Then either \(n\) is odd or \(\mathcal P\) is an elliptic quadric.