Hypersurfaces associated to Sn by a sphere congruence
In this work a sufficient condition is exhibited for a hypersurface in Rn+1 to be the envelope of a sphere congruence whose other envelope is contained in a unit sphere. A local parametrization for such envelopes is provided depending on an orthogonal local parametrization of Sn and their fundamenta...
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| Format: | Article |
| Language: | Spanish |
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Universidad Nacional de Trujillo
2019-12-01
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| Series: | Selecciones Matemáticas |
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| Online Access: | http://revistas.unitru.edu.pe/index.php/SSMM/article/view/2630 |
| Summary: | In this work a sufficient condition is exhibited for a hypersurface in Rn+1 to be the envelope of a sphere congruence whose other envelope is contained in a unit sphere. A local parametrization for such envelopes is provided depending on an orthogonal local parametrization of Sn and their fundamental forms are described. Finally, a necessary and sufficient condition is presented so that such hypersurfaces are parametrized by lines of curvature and so that they are of rotation. |
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| ISSN: | 2411-1783 2411-1783 |