Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space
type: Item
instance of: scholarly article
title: Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space
zbMATH Open document ID: 0535.53002
author: Jun-ichi Hano
author: Katsumi Nomizu
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: In a classical paper [Sur la surface de révolution dont la courbure moyenne est constante, J. Math. Pures Appl. 6, 309-320 (1841)] \textit{Ch. Delaunay} proved that the profile curve of a surface of revolution with nonzero constant mean curvature in Euclidean 3-space can be described as the locus of a focus, when a quadratic curve is rolled along the axis of revolution. In the present paper we study the problem in Lorentz- Minkowski 3-space by considering spacelike surfaces of revolution. In the case where the axis of revolution is spacelike or timelike we obtain results similar to Delaunay's except that the nature of quadrics needs special attention. In the case where the axis is a null line we can determine the profile curves completely without giving a geometric interpretation.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 3849994
zbMATH Keywords: surface of revolution
zbMATH Keywords: constant mean curvature
zbMATH Keywords: Lorentz-Minkowski space
zbMATH Keywords: quadrics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228808
OpenAlex ID: W2025948589
cites work: On isometric immersions of the hyperbolic plane into the Lorentz- Minkowski space and the Monge-Ampère equation of a certain type
cites work: A generalization of a theorem of Delaunay
cites work: Surfaces of revolution with prescribed mean curvature
DOI: 10.2748/TMJ/1178228808
description: scientific article; zbMATH DE number 3849994