Weak generalized ovoids

Determine whether every weak generalized ovoid of PG(4n − 1, q), defined as q^(2n) + 1 (n − 1)-dimensional subspaces such that every three generate a (3n − 1)-space, is a generalized ovoid.

Background

A weak generalized ovoid is defined only by the condition that every three of its (n − 1)-dimensional subspaces generate a (3n − 1)-dimensional space. A generalized ovoid, or pseudo-ovoid, additionally requires a uniquely determined tangent space at each element that is disjoint from all other elements. The paper asks whether the weaker three-generator condition implies the full generalized-ovoid structure.