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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

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.

Information

Published: 1 January 2006
First available in Project Euclid: 3 January 2019

zbMATH: 1143.53008
MathSciNet: MR2325150

Digital Object Identifier: 10.2969/aspm/04310437

Subjects:
Primary: 34C23, 53A05
Secondary: 58K25

Rights: Copyright © 2006 Mathematical Society of Japan

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