Lines of Principal Curvature on Canal Surfaces in R3
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| Format: | Artículo científico |
| Langue: | en |
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Academia Brasileira de Ciências
2006
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| _version_ | 1876423049350217728 |
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| author | Ronaldo Garcia |
| author_facet | Ronaldo Garcia |
| contents | Lines of Principal Curvature on Canal Surfaces in R3 Ronaldo Garcia Jaume Llibre Jorge Sotomayor Multidisciplinaria (Ciencias Naturales y Exactas) canal surfaces Riccati equation principal curvature lines In this paper are determined the principal curvatures and principal curvature lines on canal surfaceswhich are the envelopes of families of spheres with variable radius and centers moving along aclosed regular curve in R3. By means of a connection of the differential equations for thesecurvature lines and real Riccati equations, it is established that canal surfaces have at most twoisolated periodic principal lines. Examples of canal surfaces with two simple and one doubleperiodic principal lines are given. 2006 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32778302 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.78 |
| format | Artículo científico |
| id | redalyc_32778302 |
| institution | Redalyc |
| language | en |
| publishDate | 2006 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Lines of Principal Curvature on Canal Surfaces in R3 Ronaldo Garcia Multidisciplinaria (Ciencias Naturales y Exactas) canal surfaces Riccati equation principal curvature lines Lines of Principal Curvature on Canal Surfaces in R3 Ronaldo Garcia Jaume Llibre Jorge Sotomayor Multidisciplinaria (Ciencias Naturales y Exactas) canal surfaces Riccati equation principal curvature lines In this paper are determined the principal curvatures and principal curvature lines on canal surfaceswhich are the envelopes of families of spheres with variable radius and centers moving along aclosed regular curve in R3. By means of a connection of the differential equations for thesecurvature lines and real Riccati equations, it is established that canal surfaces have at most twoisolated periodic principal lines. Examples of canal surfaces with two simple and one doubleperiodic principal lines are given. 2006 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32778302 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.78 |
| title | Lines of Principal Curvature on Canal Surfaces in R3 |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) canal surfaces Riccati equation principal curvature lines |
| url | https://www.redalyc.org/articulo.oa?id=32778302 |