On analogs of the Reiss relation for curves on rational ruled surfaces (Q1822360)

Let an algebraic curve C of degree d in \(P^ 2(R)\) intersect a line \(\ell\) in d distinct points \(P_ i(\ell)\); \(\kappa_ i(\ell)\) be the curvature of C at \(P_ i(\ell)\), \(\theta_ i(\ell)\) be the angle from \(\ell\) to C at \(P_ i(\ell)\). Then \(\sum^{d}_{i=1}(\kappa_ i(\ell)/\sin^ 3\theta_ i(\ell)) = 0\) (Reiss relation). The author obtains a number of interesting analogs of this relation.