  We examine the effect of adding PT-symmetric gain and loss terms to quasi 1D
lattices (ribbons) that possess flat bands. We focus on three representative
cases: (a) The Lieb ribbon, (b) The kagome ribbon, and (c) The stub Ribbon. In
general we find that the effect on the flat band depends strongly on the
geometrical details of the lattice being examined. One interesting and novel
result that emerge from an analytical calculation of the band structure of the
Lieb ribbon including gain and loss, is that its flat band survives the
addition of PT-symmetry for any amount of gain and loss, while for the other
two lattices, any presence of gain and loss destroys the flat bands. For all
three ribbons, there are finite stability windows whose size decreases with the
strength of the gain and loss parameter. For the Lieb and kagome cases, the
size of this window converges to a finite value. The existence of finite
stability windows, plus the constancy of the Lieb flat band are in marked
contrast to the behavior of a pure one-dimensional lattice.
