A method is considered to induce surfaces in three‐dimensional (pseudo) Euclidean space via the solutions to two‐dimensional linear problems (20 LPs) and their integrable dynamics (deformations) via the 2 + 1‐dimensional nonlinear integrable equations associated with these 2D LPs. Coordinates X i of the induced surfaces are defined as integrals over certain bilinear combinations of the wave functions ψ of these 20 LPs. General formulation as well as three concrete examples are considered. Some properties and features of such induction are discussed. Three‐dimensional Riemann spaces associated with 2 + 1‐dimensional nonlinear integrable equations are considered also.
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B. G. Konopelchenko (1996) studied this question.
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