Helicoidal surfaces in the three-dimensional Lorentz-Minkowski space satisfying \(\Delta ^{II}r_{i} = \lambda _{i}r_{i}\)
type: Item
instance of: scholarly article
title: Helicoidal surfaces in the three-dimensional Lorentz-Minkowski space satisfying \(\Delta ^{II}r_{i} = \lambda _{i}r_{i}\)
zbMATH Open document ID: 1244.53021
published in: Journal of Geometry
publication date: 2012-01-13T00:00:00Z
review text: Consider a nondegenerate immersion \(r:M^2\rightarrow {\mathbb R}^3_1\) in three dimensional Lorentz-Minkowski space \({\mathbb R}^3_1\). It is proved that there are no helicoidal surfaces fulfilling the property \(\Delta^{\text{II}}r_i = \lambda_i r_i ~(i=1,2,3)\), where \(\lambda_i\in \mathbb R\), \(r_i:M^2\rightarrow {\mathbb R}\) are the coordinate functions of \(r\) and \(\Delta^{\text{II}}\) is the Laplacian with respect to the second fundamental form.
reviewed by: Friedrich Manhart
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 5997651
zbMATH Keywords: Lorentz-Minkowski space
zbMATH Keywords: helicoidal surfaces
zbMATH Keywords: Laplace operator
author: Chahrazéde Baba-Hamed
author: Mohammed Bekkar
MaRDI profile type: Publication
full work available at URL: s00022-011-0074-2
OpenAlex ID: W1970953989
cites work: Q4930520
cites work: Q3617817
cites work: Helicoidal surfaces in three-dimensional Minkowski space
cites work: On a certain class of finite type surfaces of revolution
cites work: An extension of Takahashi's theorem
cites work: Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying \(\Delta^{II}\vec r=A\vec r\)
cites work: Minimal immersions of Riemannian manifolds
DOI: 10.1007/S00022-011-0074-2
description: scientific article; zbMATH DE number 5997651