Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 46, No. 2, pp. 523-535 (2005)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 2, pp. 523-535 (2005) |
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Transformations for hypersurfaces with vanishing Gauss-Kronecker curvatureA. V. Corro, W. Ferreira and K. TenenblatInstituto de Matem\a'{a}tica e Estat\a'{\i}stica, Universidade Federal de Goi\a'{a}s, 74001-970 Goi\a^{a}nia, GO, Brazil e-mail: corro@mat.ufg.br, e-mail: walter@mat.ufg.br, Departamento de Matem\a'{a}tica, Universidade de Bras\a'{\i}lia 70910-900, Bras\a'{\i}lia, DF, Brazil, e-mail: keti@mat.unb.brAbstract: We provide a method of constructing families of hypersurfaces of a space form with zero Gauss-Kronecker curvature, from a given such hypersurface, based on Ribaucour transformations. Applications provide a 1-parameter family of complete, non-cylindrical hypersurfaces of $R^4$, with zero Gauss-Kronecker curvature, a 5-parameter family of compact Dupin hypersurfaces of $S^4$, with vanishing Gauss-Kronecker curvature, infinite families of hypersurfaces of $R^{n+1}$ and of the hyperbolic space $H^4$, with flat Gauss-Kronecker curvature. Full text of the article:
Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.
© 2005 Heldermann Verlag
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