Lines of Principal Curvature on Canal Surfaces in R^3

Details Lines of Principal Curvature on Canal Surfaces in R^3 Lines of Principal Curvature on Canal Surfaces in R^3

2006-04-07

arxiv.org/abs/math/0604164v1

Mathematics

Differential Geometry

11 pages

Scientific paper

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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