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Hypersurfaces with flat r-mean curvature and Ribaucour transformations

Walterson Ferreira, Keti Tenenblat


We consider Ribaucour transformations as a method of obtaining hypersurfaces with flat r-mean curvature. Solutions of an integrable system of equations provide hypersurfaces with flat Guass-Kronecker from a given such hypersurface. Nonlinear differential equations are exhibited, whose solutions provide n-dimensional hypersurfaces of the euclidean space with flat r-mean curvature. These differential equations are obtained by Ribaucour transformations applied to a totally geodesic hypersurface. Applications of the theory produce families of hypersurfaces with flat r-mean curvature.


flat r-mean curvature, Ribaucour transformations.

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