Shapiro Conjecture : Tangent and Secant Lines

Tangent and Secant Lines

Consider now the problem of lines in space that meet three lines tangent to the rational normal curve and one secant line.

As before, we first consider three tangent lines. The lines which meet these three tangents form one ruling of the hyperboloid of one sheet, and the problem reduces to determining whether or not the secant line meets the hyperboloid.