  We review a theorem by Hasse and Perlick establishing a result characterizing
parallax-free cosmological models via three equivalent properties -- namely the
existence of a redshift potential, the existence of a conformal vector field
parallel to the observer field, and the vanishing of the shear of the observer
field together with some integrability condition. We are able to provide a
simplified proof using Noether's theorem to calculate a conserved quantity
along lightlike geodesics that is connected with the conformal symmetry.
Thereby we derive more detailed information about the connection of the
kinematical invariants to the redshift isotropy and the connection of conformal
vector fields to the causality of spacetime.
