JournalsrmiVol. 24, No. 1pp. 71–90

Transformations between surfaces in R4\mathbb{R}^4 with flat normal and/or tangent bundles

  • Angel Montesinos-Amilibia

    Universitat de València, Burjassot (Valencia), Spain
Transformations between surfaces in $\mathbb{R}^4$ with flat normal and/or tangent bundles cover
Download PDF

Abstract

We exhibit several transformations of surfaces MM in R4\mathbb{R}^4: 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 ff on flat semiumbilical immersed surfaces (FSIS), such that df(TpM)df(T_pM) is totally orthogonal to TpM,T_pM, and that give FSIS. This family satisfies a Bianchi type of permutability property.

Cite this article

Angel Montesinos-Amilibia, Transformations between surfaces in R4\mathbb{R}^4 with flat normal and/or tangent bundles. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 71–90

DOI 10.4171/RMI/530