Friedrich Kottler

“ As a reference system in the sense of relativity theory, comoving with the moving point in the most general case, we have to call a system varying from location to location in such a manner, that the direction cosines of its spacelike axes are given as functions of (the arc of the world line of the moving point) by or or with , while those of its timelike axes are given by (direction cosine of the tangent) . ”

“ Regarding A it follows, that when for instance only contains spacelike directions, then as the completely perpendicular plane must also contain timelike directions (its infinitely distant line cuts the absolute measure-surface in a real way) . In our representation, must be an imaginary angle. Regarding B (1) it follows, that the rotation angle can be real or imaginary and correspondingly the displacement can be imaginary or real: cases (B) 1 and 2 of § 6. The types of curves of constant curvatures are thus obtained the same way as there. ”

“ Representation of the family as the totality of curves, which “participate” in the “windings” of the principal curve. Every point, which is fixed in the comoving tetrad, thus
where the are constants, will evidently participate in its rotation, i.e. it describes a trajectory of the family, which is definitely determined by curve . Thus the previous curves must also be representable in this shape, of which one can easily convince oneself when one computes the axes of the comoving tetrad for ”