May be you mean cylindrical coordinate lines, something that can be approached this way:

with(plots):with(plottools):
P:=changecoords(plot3d(r^2,r=0..1,phi=0..2*Pi,axes=normal),cylindrical):
C:=coordplot(polar,labelling =true,scaling=constrained):
f := transform((x, y) -> [x, y, 0]):
display({P, f(C)}, orientation=[46, 52]);