Geometry of Light Paths Between Two Material Bodies
The pattern of light signals, which was proposed before for the measurement of the curvature, is investigated in a two-dimensional manifold of constant curvature (deSitter space). The pattern consists of light signals between two freely moving bodies, each signal being emitted when the signal from the other body arrives.It is shown that the coordinates of the arrivals (or emissions) of the light signals can be obtained from the coordinates of the emission of the first signal by means of projective transformations [see Eq. (18)] which are iterates of a single such transformation. The same applies to the proper times at which these signals are received.
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