On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space
type: Item
instance of: scholarly article
title: On the Gauss map of ruled surfaces in a 3-dimensional Minkowski space
zbMATH Open document ID: 0855.53010
author: Soon Meen Choi
published in: Tsukuba Journal of Mathematics
publication date: 1997-02-03T00:00:00Z
review text: The author classifies spacelike and timelike ruled surfaces in 3-dimensional Minkowski spacetime \(\mathbb{R}^3_1\) whose Gauss map \(\xi\) satisfies \(\Delta \xi= A\xi\) for some \(3\times 3\) real matrix \(A\), where \(\Delta\) is the Laplacian of the surfaces. He proves that such surfaces are locally either \(\mathbb{R}^2_1\), \(S^1_1\times \mathbb{R}^1\), \(\mathbb{R}^1_1\times S^1\), \(\mathbb{R}^2\) or \(H^1\times \mathbb{R}^1\). Ruled surfaces in a Euclidean 3-space satisfying \(\Delta\xi= A\xi\) were classified by \textit{C. Baikoussis} and \textit{D. E. Blair} in [Glasgow Math. J. 34, No. 3, 355-359 (1992; Zbl 0762.53004)]. Ruled surfaces of finite type in a Euclidean \(n\)-space in general were completely classified by \textit{C. Baikoussis}, the reviewer and \textit{L. Verstraelen} in [Tokyo J. Math. 16, No. 2, 341-349 (1993; Zbl 0798.53055)].
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 895938
zbMATH Keywords: Minkowski space
zbMATH Keywords: ruled surfaces
zbMATH Keywords: Gauss map
zbMATH Keywords: Laplacian
zbMATH Keywords: surfaces of finite type
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162870
OpenAlex ID: W1649643265
DOI: 10.21099/TKBJM/1496162870
description: scientific article; zbMATH DE number 895938