Irrotational vector fields, partially invariant with respect to group of rotations

A geometrical description of three-dimensional irrotational vector fields which are partially invariant with respect to the SO(3) group of rotations is given. It is shown that the motion of a continuum, that satisfies the equation of continuity and is partially invariant with respect to SO(3), is necessarily rotational, that is, the curl of the velocity vector is non zero.