#### Vol. 3, No. 1, 2006

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A subset of the Hermitian surface

### Giorgio Donati and Nicola Durante

Vol. 3 (2006), No. 1, 13–23
##### Abstract

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

##### Keywords
Hermitian surface, collineation
##### Mathematical Subject Classification 2000
Primary: 05B25, 51E20