  We consider fermion systems on a square lattice with a mass term having a
curved domain-wall. Similarly to the conventional flat domain-wall fermions,
massless and chiral edge states appear on the wall. In the cases of $S^1$ and
$S^2$ domain-walls embedded into flat hypercubic lattices, we find that these
edge modes feel gravity through the induced Spin or Spin$^c$ connections. The
gravitational effect is encoded in the Dirac eigenvalue spectrum as a gap from
zero. In the standard continuum extrapolation of the square lattice, we find a
good agreement with the analytic prediction in the continuum theory. We also
find that the rotational symmetry of the edge modes is automatically recovered
in the continuum limit.
