  The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is
obtained from the Euclidean space by substituting the usual Euclidean distance
with the isotropic distance. In the present paper, we give several
classifications on the surfaces in I^3 with the constant relative curvature
(analogue of the Gaussian curvature) and the constant isotropic mean curvature.
In particular, we classify the helicoidal surfaces in I^3 with constant
curvature and analyze some special curves on these.
