Ribaucour Transformations for Hypersurfaces in Space Forms |
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Authors: | Keti Tenenblat Qiaoling Wang |
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Institution: | (1) Departamento de Matemática-IE., Universidade de Brasília, Campus Universitário, 70910–900 Brasília-DF, Brasil |
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Abstract: | The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20. |
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Keywords: | Ribaucour transformations constant mean curvature surfaces minimal surfaces space forms |
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