Generalized Weierstrass representation for surfaces in multidimensional   Riemann spaces
  Generalizations of the Weierstrass formulae to generic surface immersed into $R^4$, $S^4$ and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed. 
B.G. Konopelchenko, G. Landolfi