Illinois Journal of Mathematics

Minimal hypersurfaces with zero Gauss-Kronecker curvature

T. Hasanis, A. Savas-Halilaj, and T. Vlachos

Full-text: Open access

Abstract

We investigate complete minimal hypersurfaces in the Euclidean space ${R}^{4}$, with Gauss-Kronecker curvature identically zero. We prove that, if $f:M^{3}\rightarrow {R}^{4}$ is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below, then $f(M^{3})$ splits as a Euclidean product $L^{2}\times {R}$, where $L^{2}$ is a complete minimal surface in $ {R}^{3}$ with Gaussian curvature bounded from below.

Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 523-529.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138032

Digital Object Identifier
doi:10.1215/ijm/1258138032

Mathematical Reviews number (MathSciNet)
MR2164350

Zentralblatt MATH identifier
1087.53056

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Hasanis, T.; Savas-Halilaj, A.; Vlachos, T. Minimal hypersurfaces with zero Gauss-Kronecker curvature. Illinois J. Math. 49 (2005), no. 2, 523--529. doi:10.1215/ijm/1258138032. https://projecteuclid.org/euclid.ijm/1258138032


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