Collineations and motions in self-gravitating magnetofluids

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Abstract
For the self‐gravitating magnetofluid admitting a Ricci collineation with respect to the flow vector, it is proved that (i) the stream lines are expansion‐free if and only if the heat‐flux vector is divergence‐free; (ii) the stream lines are geodesic if and only if the heat‐flux vector remains invariant along the system of stream lines. The affine collineation with respect to the geodesic and expansion‐free flow of the magnetofluid is a motion. Conformal motions with respect to the flow vector, the magnetic field vector, and the heat flux vector are investigated.