Characterizing parabolic hyperplanes of the hyperbolic and elliptic quadrics in PG(2n + 1, q)

In this article, a combinatorial characterization of the family of parabolic hyperplanes of a hyperbolic (respectively, elliptic) quadric of PG(2n + 1, q), using their intersection properties with the points and subspaces of codimension 2, is given.