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 |
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| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652004000400002 |
| Summary: | 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. |
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| ISSN: | 0001-3765 1678-2690 |