Hypersurfaces with prescribed curvatures in the de Sitter space
type: Item
instance of: scholarly article
title: Hypersurfaces with prescribed curvatures in the de Sitter space
zbMATH Open document ID: 1493.53092
DOI: 10.4171/RMI/1279
author: Ángela Roldán
published in: Revista Matemática Iberoamericana
publication date: 2022-03-25T00:00:00Z
review text: Summary: In this paper, we establish a relationship between spacelike hypersurfaces in the de Sitter space \(\mathbb{S}_1^{n+1}\) and conformal metrics on the sphere \(\mathbb{S}^n\). As a consequence of this relation and some deep results in conformal geometry, we classify spacelike hypersurfaces in \(\mathbb{S}_1^{n+1}\) satisfying certain global conditions and a very general Weingarten relation \(W(k_1,\dots,k_n)= 0\) of elliptic type, where \(k_1,\dots,k_n\) are its principal curvatures. Also, we particularize to some important cases as the \(r\)th mean curvatures.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 7498316
zbMATH Keywords: space-like hypersurfaces
zbMATH Keywords: de Sitter space
zbMATH Keywords: conformal metrics
zbMATH Keywords: Weingarten hypersurfaces
zbMATH Keywords: higher-order mean curvatures
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7498316