GAUSS-CODAZZI-EQUATIONS FOR GENERIC SURFACES - EQUIVALENCE TO THE DS LINEAR PROBLEM WITH CONSTRAINT, LINEARIZABILITY AND REDUCTIONS

It is shown that the standard Gauss-Codazzi system of equations which describe generic surfaces immersed into the three-dimensional Euclidea n space is equivalent to the two-dimensional Dirac equation (Davey-Ste wartson linear problem) accompanied by a specific constraint. It is de monstrated that this system is linearizable via the parametrization of the moving trihedral by the Euler angles. Some special classes of sur faces are also considered.