Generalized Weierstrass-Enneper inducing, conformal immersions, and gravity

Basic quantities related to 2D gravity, such as Polyakov extrinsic action, Nambu-Goto action, geometrical action and the Euler characteristic, are studied using generalized Weierstrass-Enneper (GWE) inducing of surfaces in R(3). Connection of the GWE inducing with conformal immersion is made and various aspects of the theory are shown to be invariant under the modified Veselov-Novikov hierarchy of flows. The geometry of h root g = 1 surfaces (h similar to mean curvature) is shown to be connected with the dynamics of infinite- and finite-dimensional integrable systems. Connections with Liouville-Beltrami gravity are indicated.