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

TL;DR

This paper provides a combinatorial characterization of parabolic hyperplanes in hyperbolic and elliptic quadrics within projective geometry, based on their intersection properties with points and subspaces.

Contribution

It introduces a novel combinatorial method to identify parabolic hyperplanes in hyperbolic and elliptic quadrics in PG(2n+1, q).

Findings

Characterization of parabolic hyperplanes using intersection properties

Applicable to hyperbolic and elliptic quadrics in PG(2n+1, q)

Enhances understanding of geometric structures in projective spaces

Abstract

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.