ABSTRACT
Consider PG(4,K), for K a field admitting a quadratic extension field K+ and let
Q4 : Q4(x1, x2, y1, y2, z) = x1y2 − x2y1 − γz 2,
for γ a constant, be a non-degenerate quadric in PG(4,K). Note that if Σ3 ' PG(3,K) is given by z = 0, then Q4∩Σ3 in a regulus in Σ3. Consider the mapping
eα : (x1, x2, y1, y2, z) 7−→ (x1, x2, x1α + y1, x2α + y2, z), for α ∈ K.
