Abstract

In this paper we define a ruled algebraic surface of $PG\left(3,q^2\right)$, called a hyperbolic ${\mathcal{Q}}_{\mathcal{ℱ}}$-set and we prove that it is contained in the Hermitian surface of $PG\left(3,q^2\right)$. Also, we characterise a hyperbolic ${\mathcal{Q}}_{\mathcal{ℱ}}$-set as the intersection of two Hermitian surfaces.

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Mathematical Subject Classification 2000

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