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

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