We exhibit several transformations of surfaces in : a transformation of flat surfaces that gives surfaces with flat normal bundle (semiumbilical surfaces); and its inverse that from a semiumbilical surface obtains a flat surface; then a one-parameter family of transformations on flat semiumbilical immersed surfaces (FSIS), such that is totally orthogonal to and that give FSIS. This family satisfies a Bianchi type of permutability property.
Cite this article
Angel Montesinos-Amilibia, Transformations between surfaces in with flat normal and/or tangent bundles. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 71–90DOI 10.4171/RMI/530