Non-closed minimal hypersurfaces of $S^4(1)$ with identically zero Gauss-Kronecker curvature

Source file is available as :   Postscript Document

Author(s) : Tsasa Lusala

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 747-2002

MSC 2000

53B25 Local submanifolds
53C40 Global submanifolds

Abstract :
We give a partial local description of minimal hypersurfaces $M^3$ with identically zero Gau\ss-Kronecker curvature function in the unit $4$-sphere $S^4{1}$, without assumption on the compactness of $M^3$.

Keywords : Minimal hypersurfaces in spheres, isoparametric hypersurfaces, identically zero Gauss-Kronecker curvature, nowhere zero second fundamental form.