Contributions to the theory of the axes of curvature (Q1386329)

In the theory of the axes of curvature in space kinematics, we distinguish the axis of curvature with respect to a trajectory curve and the axis of curvature with respect to a trajectory ruled surface. The first case was studied by \textit{E. Stübler} [Jahresber. DMV 19, 177--185 (1910; JFM 41.0771.03; JFM 41.0802.02)], the second one by \textit{M. Disteli} [Z. Math. Phys. 62, 261--309 (1914; JFM 45.0959.01)]. In this paper, the author examines at first some nice metric properties concerning the axis of curvature of a path. Then he gives an elegant new construction of the Disteli-axis which makes no use of the Disteli-axes of the instantaneous axodes. Furthermore, in connection with the Disteli-axis of a trajectory ruled surface, the author investigates some metric properties of the induced line correspondence and gives a new characterization of the vertex congruence.