  It is well-known that the theory of Cotton gravity proposed by Harada is
trivially solved by all isotropic and homogeneous cosmologies. We show that
this under-determination is more general. More precisely, the degree of
arbitrariness in the solutions increases with the degree of symmetry. We give
two simple examples. The first is that of static spherically symmetric
solutions, which depend on an arbitrary function of the radial coordinate. The
second is that of anisotropic cosmologies, which depend on an arbitrary
function of time.
