Tohoku Mathematical Journal

Contact properties of surfaces in ${\mathbb R}^3$ with corank 1 singularities

Abstract

We study the geometry of surfaces in $\mathbb{R}^3$ with corank 1 singularities. At a singular point we define the curvature parabola using the first and second fundamental forms of the surface, which contains all the local second order geometrical information about the surface. The curvature parabola is used to introduce the concepts of asymptotic directions and umbilic curvature, which are related to contact properties of the surface with planes and spheres.

Article information

Source
Tohoku Math. J. (2), Volume 67, Number 1 (2015), 105-124.

Dates
First available in Project Euclid: 20 April 2015

https://projecteuclid.org/euclid.tmj/1429549581

Digital Object Identifier
doi:10.2748/tmj/1429549581

Mathematical Reviews number (MathSciNet)
MR3337965

Zentralblatt MATH identifier
1320.58023

Citation

Martins, Luciana F.; Nuño-Ballesteros, Juan J. Contact properties of surfaces in ${\mathbb R}^3$ with corank 1 singularities. Tohoku Math. J. (2) 67 (2015), no. 1, 105--124. doi:10.2748/tmj/1429549581. https://projecteuclid.org/euclid.tmj/1429549581

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