A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere
In this note we will show that the inverse image under the stereographic projection of a circular torus of revolution in the 3-dimensional euclidean space has constant mean curvature in the unit 3-sphere if and only if their radii are the catet and the hypotenuse of an appropriate right triangle.<...
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| Format: | Article |
| Language: | English |
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Academia Brasileira de Ciências
2004-12-01
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| Series: | Anais da Academia Brasileira de Ciências |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000400002 |
| _version_ | 1819198384096935936 |
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| author | Abdênago Barros |
| author_facet | Abdênago Barros |
| author_sort | Abdênago Barros |
| collection | DOAJ |
| description | In this note we will show that the inverse image under the stereographic projection of a circular torus of revolution in the 3-dimensional euclidean space has constant mean curvature in the unit 3-sphere if and only if their radii are the catet and the hypotenuse of an appropriate right triangle.<br>Neste artigo mostraremos que a imagem inversa pela projeção estereográfica de um toro circular de revolução no espaço euclidiano de dimensão 3 tem curvatura média constante se e somente se os seus raios são o cateto e a hipotenusa de um triângulo retângulo apropriado. |
| first_indexed | 2024-12-23T02:59:35Z |
| format | Article |
| id | doaj.art-17b91d32719043f3970652e68616d5aa |
| institution | Directory Open Access Journal |
| issn | 0001-3765 1678-2690 |
| language | English |
| last_indexed | 2024-12-23T02:59:35Z |
| publishDate | 2004-12-01 |
| publisher | Academia Brasileira de Ciências |
| record_format | Article |
| series | Anais da Academia Brasileira de Ciências |
| spelling | doaj.art-17b91d32719043f3970652e68616d5aa2022-12-21T18:02:28ZengAcademia Brasileira de CiênciasAnais da Academia Brasileira de Ciências0001-37651678-26902004-12-0176463964310.1590/S0001-37652004000400002A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphereAbdênago BarrosIn this note we will show that the inverse image under the stereographic projection of a circular torus of revolution in the 3-dimensional euclidean space has constant mean curvature in the unit 3-sphere if and only if their radii are the catet and the hypotenuse of an appropriate right triangle.<br>Neste artigo mostraremos que a imagem inversa pela projeção estereográfica de um toro circular de revolução no espaço euclidiano de dimensão 3 tem curvatura média constante se e somente se os seus raios são o cateto e a hipotenusa de um triângulo retângulo apropriado.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000400002Toro planoCurvatura média constanteToro circularProjeção estereográficaFlat torusconstant mean curvaturecircular toristereographic projection |
| spellingShingle | Abdênago Barros A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere Anais da Academia Brasileira de Ciências Toro plano Curvatura média constante Toro circular Projeção estereográfica Flat torus constant mean curvature circular tori stereographic projection |
| title | A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere |
| title_full | A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere |
| title_fullStr | A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere |
| title_full_unstemmed | A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere |
| title_short | A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere |
| title_sort | relation between the right triangle and circular tori with constant mean curvature in the unit 3 sphere |
| topic | Toro plano Curvatura média constante Toro circular Projeção estereográfica Flat torus constant mean curvature circular tori stereographic projection |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000400002 |
| work_keys_str_mv | AT abdenagobarros arelationbetweentherighttriangleandcirculartoriwithconstantmeancurvatureintheunit3sphere AT abdenagobarros relationbetweentherighttriangleandcirculartoriwithconstantmeancurvatureintheunit3sphere |