Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 2, pp. 523-535 (2005)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Transformations for hypersurfaces with vanishing Gauss-Kronecker curvature

A. V. Corro, W. Ferreira and K. Tenenblat

Instituto 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:, e-mail:, Departamento de Matem\a'{a}tica, Universidade de Bras\a'{\i}lia 70910-900, Bras\a'{\i}lia, DF, Brazil, e-mail:

Abstract: 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
© 2005–2008 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition