Hypersurfaces in non-flat pseudo-Riemannian space forms satisfying a linear condition in the linearized operator of a higher order mean curvature
type: Item
instance of: scholarly article
title: Hypersurfaces in non-flat pseudo-Riemannian space forms satisfying a linear condition in the linearized operator of a higher order mean curvature
zbMATH Open document ID: 1283.53067
author: Pascual Lucas
author: H. Fabian Ramirez-Ospina
published in: Taiwanese Journal of Mathematics
publication date: 2013-04-25T00:00:00Z
full work available at URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/1738
review text: The authors study the geometry of hypersurfaces in a pseudo-Riemannian de Sitter or anti-de Sitter space. They prove a classification theorem for hypersurfaces satisfying a linear condition in the linearized operator of a higher-order mean curvature. In the proof of the theorem, the authors introduce new techniques based on the complexification of the shape operator of a hypersurface.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 6157589
zbMATH Keywords: linearized operator \(L_k\)
zbMATH Keywords: isoparametric hypersurface
zbMATH Keywords: \(k\)-maximal hypersurface
zbMATH Keywords: Takahashi theorem
zbMATH Keywords: higher-order mean curvatures
zbMATH Keywords: Newton transformations
reviewed by: Aurel Bejancu
MaRDI profile type: Publication
OpenAlex ID: W2061402638
Wikidata QID: Q115243011
DOI: 10.11650/TJM.17.2013.1738
description: scientific article; zbMATH DE number 6157589