  In [DM] it was asked whether all flat holomorphic Cartan geometries (G,H) on
a complex torus are translation invariant. We answer this affimatively under
the assumption that the complex Lie group G is affine. More precisely, we show
that every holomorphic Cartan geometry of type (G,H), with G a complex affine
Lie group, on any complex torus is translation invariant.
