Application of soliton theory to the construction of isometric immersions of \(M^{n_1}(c_1)\times M^{n_2}(c_2)\) into constant curvature spaces \(M^n(\pm 1)\). (Q1565994)

The integrability condition for constant curvature surfaces in 3-space is the sine- or sinh-Gordon equation. But also in higher dimensions and codimensions the integrability conditions of constant curvature immersions can be formulated as a zero curvature condition and treated by finite gap soliton theory as developed in [\textit{D. Ferus} and \textit{F. Pedit}, Math. Ann. 305, 329--342 (1996; Zbl 0866.53046)]. The author uses this method to immerse products of constant curvature spaces using a 2-parameter loop algebra.