Abstract:
Let H be a non-empty set of hyperplanes in PG(4, q), q even, such that every point of PG(4, q) lies in either 0, 1 2 q3 or 1 2 (q3 + q2) hyperplanes of H, and every plane of PG(4, q) lies in 0 or at least 1 2 q hyperplanes of H. Then H is the set of all hyperplanes which meet a given non-singular quadric Q(4, q) in a hyperbolic quadric.
