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Lines of principal curvature on canal surfaces in R³

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Author(s): Garcia Ronaldo | Llibre Jaume | Sotomayor Jorge

Journal: Anais da Academia Brasileira de Ciências
ISSN 0001-3765

Volume: 78;
Issue: 3;
Start page: 405;
Date: 2006;
Original page

Keywords: Riccati equation | principal curvature lines | canal surfaces

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 R³. 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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