  In the previous report (J. Phys. A (1997) 30 4019-4029), I showed that the
Dirac operator defined over a conformal surface immersed in R^3 is identified
with the Dirac operator which is generalized the Weierstrass- Enneper equation
and Lax operator of the modified Novikov-Veselov (MNV) equation. In this
article, I determine the Dirac operator defined over a conformal surface
immersed in R^4, which is reduced to the Lax operators of the nonlinear
Schrodinger and the MNV equations by taking appropriate limits. Thus the Dirac
operator might be the Lax operator of (2+1)- dimensional soliton equation.
