Friedrich Kottler

“ The metric nature of the relativity principle suggests the consideration of the metrically preferred ones under the possible spacetime lines; these are the ones which allow a shift into themselves, and whose three curvatures are thus constant. Those as well as a second class of curves, the parallel curves representing the orthogonal trajectories of spaces, have already been studied by Herglotz in his work on the Born rigid body. ”

“ The previously mentioned two classes of curves will be shown to be the trajectory curves of a radius vector which is fixed in the comoving tetrad of the principal curve. The application to the world lines shows, that the mentioned constancy of the fields with respect to the first class takes place in the comoving tetrad of the light-point or of the reference-point – when reciprocity is present for both of them, so that the shape of the charge whose points possess such world lines can be seen as constant in this reference system. ”