Feet in Orthogonal-Buekenhout-Metz Unitals

Abstract

Given an Orthogonal-Buekenhout-Metz unital $U_{\alpha ,\beta }$, embedded in $PG(2,q^2)$, and a point $P\notin U_{\alpha ,\beta }$, we study the set of feet, ${\tau }_P(U_{\alpha ,\beta })$, of $P$ in $U_{\alpha ,\beta }$. We characterize geometrically each of these sets as either $q+1$ collinear points or as $q+1$ points partitioned into two arcs. Other results about the geometry of these sets are also given.

11 pages, 0 figures