JournalsrmiVol. 26, No. 3pp. 799–824

Contact properties of codimension 2 submanifolds with flat normal bundle

  • Juan José Nuño Ballesteros

    Universitat de València, Burjassot (Valencia), Spain
  • María Carmen Romero Fuster

    Universitat de València, Burjassot (Valencia), Spain
Contact properties of codimension 2 submanifolds with flat normal bundle cover

Abstract

Given an immersed submanifold MnRn+2M^n\subset\mathbb{R}^{n+2}, we characterize the vanishing of the normal curvature RDR_D at a point pMp \in M in terms of the behaviour of the asymptotic directions and the curvature locus at pp. We relate the affine properties of codimension 2 submanifolds with flat normal bundle with the conformal properties of hypersurfaces in Euclidean space. We also characterize the semiumbilical, hypespherical and conformally flat submanifolds of codimension 2 in terms of their curvature loci.

Cite this article

Juan José Nuño Ballesteros, María Carmen Romero Fuster, Contact properties of codimension 2 submanifolds with flat normal bundle. Rev. Mat. Iberoam. 26 (2010), no. 3, pp. 799–824

DOI 10.4171/RMI/617