Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 2, pp. 523535 (2005) 

Transformations for hypersurfaces with vanishing GaussKronecker 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, 74001970 Goi\a^{a}nia, GO, Brazil email: corro@mat.ufg.br, email: walter@mat.ufg.br, Departamento de Matem\a'{a}tica, Universidade de Bras\a'{\i}lia 70910900, Bras\a'{\i}lia, DF, Brazil, email: keti@mat.unb.brAbstract: We provide a method of constructing families of hypersurfaces of a space form with zero GaussKronecker curvature, from a given such hypersurface, based on Ribaucour transformations. Applications provide a 1parameter family of complete, noncylindrical hypersurfaces of $R^4$, with zero GaussKronecker curvature, a 5parameter family of compact Dupin hypersurfaces of $S^4$, with vanishing GaussKronecker curvature, infinite families of hypersurfaces of $R^{n+1}$ and of the hyperbolic space $H^4$, with flat GaussKronecker curvature. Full text of the article:
Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.
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