On Tzitzeica surfaces (Q2743701)

For a twisted curve in the Euclidean 3-space we denote the distance of its osculating plane from the origin \(O\) by \(d\), its radius of torsion by \(T\). For a surface the symbol \(K\) may denote the total curvature, \(p\) the distance of the corresponding tangent plane from \(O\). G. Tzitzeica has studied curves and surfaces with the properties \(T d^2 = \text{const.}\) (Tzitzeica-curves) and \(K p^{-4} = \text{const.}\) (Tzitzeica-surfaces). The paper delivers a short proof and a generalisation of the statement, that the asymptotic lines of a Tzitzeica-surface are Tzitzeica-curves.