Characterising hyperbolic hyperplanes of a non-singular quadric in PG(4,q)

2019/06/04 by Barwick, S. G., Hui, Alice M. W., Jackson, Wen-Ai +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.04932

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, \frac12q³ or \frac12(q³+q²) hyperplanes of H, and every plane of PG(4,q) lies in 0 or at least \frac12q 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.

Cited by

• Characterization of non-singular hyperplanes of H(s,q²) in P G(s, q²)

Related

• A characterization of the planes meeting a hyperbolic quadric of \PG(3,q) in a conic
• Characterising elliptic and hyperbolic hyperplanes of the parabolic\n quadric Q(2n,q)
• Characterizing parabolic hyperplanes of the hyperbolic and elliptic quadrics in PG(2n + 1, q)
• Characterising elliptic solids of Q(4,q), q even
• Intersection of two quadrics with no common hyperplane in ℙⁿ(\mathbbF_q)