Lines of principal curvature near singular end points of surfaces in $\mathbb{R}^3$

Sotomayor, Jorge; Garcia, Ronaldo

doi:10.2969/aspm/04310437

VOL. 43 | 2006 Lines of principal curvature near singular end points of surfaces in $\mathbb{R}^3$

Jorge Sotomayor, Ronaldo Garcia

Editor(s) Shyuichi Izumiya, Goo Ishikawa, Hiroo Tokunaga, Ichiro Shimada, Takasi Sano

Adv. Stud. Pure Math., 2006: 437-462 (2006) DOI: 10.2969/aspm/04310437

Abstract

In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean 3–space near their end points, at which the surfaces tend to infinity.

This is a natural complement and extension to smooth surfaces of the work of Garcia and Sotomayor (1996), devoted to the study of principal curvature nets which are structurally stable –do not change topologically– under small perturbations on the coefficients of the equations defining algebraic surfaces.

This paper goes one step further and classifies the patterns of the most common and stable behaviors at the ends, present also in generic families of surfaces depending on one-parameter.