Affine curvature lines of surfaces in 3-space

Abstract

In this work we study the affine principal lines of surfaces in 3-space. We consider the binary differential equation of the affine curvature lines and obtain the topological models of these curves near the affine umbilic points (elliptic and hyperbolic). We also describe the generic behavior of affine curvature lines in the neighborhood of points with double eigenvalues (but not umbilics) of the affine shape operator and parabolic points

arXiv comment31 pages, 9 figures

References in corpus (1)

• Improper affine spheres and the Hessian one equation

Cited by in corpus (1)

• Singularities of 3-parameter line congruences in ${\mathbb{R}}^4$