Explicit construction for local isometric immersions of space forms (Q1812241)

Isometric immersions of space forms have been one of basic problems in differential geometry. According to \textit{J. D. Moore} [Pac. J. Math. 40, 157--166 (1972; Zbl 0238.53033)], isometric immersions of space forms \(M^n(c)\) of curvature \(c\) into the space forms \(M^{2n-1}(\tilde{c})\) with \(c<\tilde{c}\) must have flat normal bundle and linearly independent curvature normals. In the paper under review, the authors study local isometric immersions \(M^n(c) \rightarrow M^{2n-1}(c+\epsilon^2)\) by means of soliton techniques. The explicit constructions are given for this problem via Darboux transformations and some examples are included.