Lines of principal curvature on canal surfaces in ℝ3

Ronaldo Garcia, Jaume Llibre, Jorge Sotomayor

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5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)405-415
JournalAnais da Academia Brasileira de Ciencias
Issue number3
Publication statusPublished - 1 Jan 2006


  • Canal surfaces
  • Principal curvature lines
  • Riccati equation

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