Lines of principal curvature on canal surfaces in R³
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Academia Brasileira de Ciências
2006-01-01
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| Series: | Anais da Academia Brasileira de Ciências |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652006000300002 |
| Summary: | 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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| ISSN: | 0001-3765 1678-2690 |