Self-duality of pseudo-ovals

Determine whether every pseudo-oval in PG(3n − 1, q) for odd q is isomorphic to its translation dual.

Background

For odd q, the tangent spaces of a pseudo-oval form a dual pseudo-oval, called its translation dual. The paper establishes the construction of this dual object but leaves open whether the original pseudo-oval and its translation dual must always be isomorphic.