Revista Matemática Iberoamericana

Contact properties of codimension 2 submanifolds with flat normal bundle

J. J. Nuño-Ballesteros and M. C. Romero-Fuster

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 26, Number 3 (2010), 799-824.

Dates
First available in Project Euclid: 27 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1282913822

Mathematical Reviews number (MathSciNet)
MR2789366

Zentralblatt MATH identifier
1205.53007

Subjects
Primary: 53A05: Surfaces in Euclidean space 58C25: Differentiable maps

Keywords
asymptotic directions $\nu$-principal curvature foliation umbilicity sphericity normal curvature

Citation

Nuño-Ballesteros, J. J.; Romero-Fuster, M. C. Contact properties of codimension 2 submanifolds with flat normal bundle. Rev. Mat. Iberoamericana 26 (2010), no. 3, 799--824. https://projecteuclid.org/euclid.rmi/1282913822


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