Communications in Analysis and Geometry

Volume 17 (2009)

Number 4

$3$-manifolds in Euclidean space from a contact viewpoint

Pages: 755 – 776

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n4.a8

Authors

María del Carmen Romero-Fuster (Departament de Geometria i Topologia, Universitat de València, Spain)

Ana Claudia Nabarro (Depto. de Matemática, ICMC- Universidade de São Paulo, Brazil)

Abstract

We study the geometry of $3$-manifolds generically embedded in$\mathbb{R}^n$ by means of the analysis of the singularities of thedistance-squared and height functions on them. We describe thelocal structure of the discriminant (associated to thedistribution of asymptotic directions), the ridges and the flatridges.

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