INDUCED SURFACES AND THEIR INTEGRABLE DYNAMICS

A method is considered to induce surfaces in three-dimensional (pseudo ) Euclidean space via the solutions to two-dimensional linear problems (2D LPs) and their integrable dynamics (deformations) via the 2 + 1-d imensional nonlinear integrable equations associated with these 2D LPs . Coordinates X(i) of the induced surfaces are defined as integrals ov er certain bilinear combinations of the wave functions psi of these 2D LPs. General formulation as well as three concrete examples are consi dered. Some properties and features of such induction are discussed. T hree-dimensional Riemann spaces associated with 2 + 1-dimensional nonl inear integrable equations are considered also.