Lines of principal curvature on canal surfaces in R3
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Data
2006
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Resumo
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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Palavras-chave
Riccati equation, Principal curvature lines, Canal surfaces, Equação de Riccati, Linha de curvatura principal, Superfície canal
Citação
GARCIA, Ronaldo Alves; SOTOMAYOR, Jorge; LLIBRE, Jaume. Lines of principal curvature on canal surfaces in R3. Anais da Academia Brasileira de Ciências, Rio de Janeiro, v. 78, n. 2, p. 405-415, 2006.