Revista Matemática Iberoamericana


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Volume 26, Issue 3, 2010, pp. 799–824
DOI: 10.4171/RMI/617

Published online: 2010-12-31

Contact properties of codimension 2 submanifolds with flat normal bundle

Juan José Nuño Ballesteros[1] and María Carmen Romero Fuster[2]

(1) Universitat de València, Burjassot (Valencia), Spain
(2) Universitat de València, Burjassot (Valencia), Spain

Given an immersed submanifold $M^n\subset\mathbb{R}^{n+2}$, we characterize the vanishing of the normal curvature $R_D$ at a point $p \in M$ in terms of the behaviour of the asymptotic directions and the curvature locus at $p$. 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.

Keywords: Asymptotic directions, ν-principal curvature foliation, umbilicity, sphericity, normal curvature

Nuño Ballesteros Juan José, Romero Fuster María Carmen: Contact properties of codimension 2 submanifolds with flat normal bundle. Rev. Mat. Iberoamericana 26 (2010), 799-824. doi: 10.4171/RMI/617