Lines of Principal Curvature on Canal Surfaces in R^3
Differential Geometry
2007-05-23 v1 Dynamical Systems
Abstract
In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R^3. By means of a connection of the differential equations for these curvature lines and real Riccati equations, it is established that canal surfaces have at most two isolated periodic principal lines. Examples of canal surfaces with two simple and one double periodic principal lines are given.
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Cite
@article{arxiv.math/0604164,
title = {Lines of Principal Curvature on Canal Surfaces in R^3},
author = {Ronaldo Garcia and Jaume Llibre and Jorge Sotomayor},
journal= {arXiv preprint arXiv:math/0604164},
year = {2007}
}
Comments
11 pages