M. M. Diniz, J. A. Vilhena, J. F. Zapata, “Minimal hypersurfaces in <nobr>$\mathbb{S}^5$</nobr> with vanishing Gauss–Kronecker curvature”, Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 3,Pages <nobr>31

This article is cited in 1 paper

Minimal hypersurfaces in $\mathbb{S}^5$ with vanishing Gauss–Kronecker curvature

M. M. Diniz^a, J. A. Vilhena^a, J. F. Zapata^b

^a Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará
^b Universidade de São Paulo, Escola de Engenharia de Lorena

Abstract: We give a local description of complete minimal hypersurfaces in $\mathbb{S}^5$ with zero Gauss–Kronecker curvature, zero $3$-mean curvature and nowhere-zero second fundamental form.

Keywords: minimal hypersurfaces, Gauss–Kronecker curvature, complete hypersurfaces.

UDC: 714.76

MSC: 53C42

Received: 19.08.2016
Revised: 21.04.2017

DOI: 10.4213/im8597