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A Characterization of the Complement of the Hyperbolic Quadric in PG (3, q) | Synapse

April 24, 2026

A Characterization of the Complement of the Hyperbolic Quadric in PG (3, q)

Key Points

The aim is to characterize the complement of the hyperbolic quadric in PG(3,q).
Analyzed the set of points related to hyperbolic quadrics in projective geometry.
Generalized results from previous studies on planes intersecting hyperbolic quadrics.
Presented a new characterization of the complement of the hyperbolic quadric.
Generalized a result on non tangent planes to the hyperbolic quadric in PG(3,q).

Abstract

In this paper, we present a characterization of the complement of the set of points of a hyperbolic quadric of PG(3, q). As a byproduct we obtain a generalization of a recent result of B. Sahu A characterisation of the planes meeting a hyperbolic quadric of PG(3, q) in a conic, Austral. J. Combin. 84 (1), (2022) 178-186 characterizing the set of non tangent planes to a hyperbolic quadric of PG(3, q).

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Cite This Study

Vito Napolitano (Wed,) studied this question.

synapsesocial.com/papers/69eb0a2e553a5433e34b4587 https://doi.org/https://doi.org/10.36890/iejg.1714677

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