Regularity of pseudo-ovals and pseudo-hyperovals

Determine whether every pseudo-oval and every pseudo-hyperoval in the relevant finite projective spaces is regular.

Background

Pseudo-ovals and pseudo-hyperovals generalize ovals and hyperovals by replacing points with (n − 1)-dimensional subspaces. Regular, or elementary, examples arise by field reduction from ovals or hyperovals over an extension field. The paper states that every known example is regular, but does not establish that regularity is universal.