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September, 2010 Contact properties of codimension 2 submanifolds with flat normal bundle
J. J. Nuño-Ballesteros , M. C. Romero-Fuster
Rev. Mat. Iberoamericana 26(3): 799-824 (September, 2010).

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.

Citation

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J. J. Nuño-Ballesteros . M. C. Romero-Fuster . "Contact properties of codimension 2 submanifolds with flat normal bundle." Rev. Mat. Iberoamericana 26 (3) 799 - 824, September, 2010.

Information

Published: September, 2010
First available in Project Euclid: 27 August 2010

zbMATH: 1205.53007
MathSciNet: MR2789366

Subjects:
Primary: 53A05, 58C25

Rights: Copyright © 2010 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.26 • No. 3 • September, 2010
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