Rotational surfaces in a pseudo-Riemannian 3-sphere
type: Item
instance of: scholarly article
title: Rotational surfaces in a pseudo-Riemannian 3-sphere
zbMATH Open document ID: 0592.53047
author: Hiroshi Mori
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: Let \(S^ 3_ 1(c)\) be a pseudo-Riemannian 3-sphere of constant positive sectional curvature c. For every constant \(h>1\) the author constructs some families of complete, space-like, rotational surfaces in \(S^ 3_ 1(1)\) with constant mean curvature h, none of which are umbilical. According to a theorem of \textit{K. Akutagawa} (On space-like hypersurfaces with constant mean curvature in the de Sitter space, preprint), if M is a complete, space-like hypersurface with constant mean curvature h in \(S^ 3_ 1(c)\) such that \(| h| \leq c^{1/2}\) then M is totally umbilical. Thus the author's construction shows that the estimate is sharp.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 3951495
zbMATH Keywords: umbilical hypersurface
zbMATH Keywords: pseudo-Riemannian 3-sphere
zbMATH Keywords: constant mean curvature
zbMATH Keywords: space-like hypersurface
Wikidata QID: Q115227211
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228534
OpenAlex ID: W1968621184
cites work: Q3072862
cites work: Q5678153
cites work: Rotation Hypersurfaces in Spaces of Constant Curvature
cites work: Q3717746
cites work: Stable Complete Constant Mean Curvature Surfaces in R 3 and H 3
cites work: Q5546515
DOI: 10.2748/TMJ/1178228534
description: scientific article; zbMATH DE number 3951495