\(E^3\)-complete timelike surfaces in \(E_1^3\) are globally hyperbolic
type: Item
instance of: scholarly article
title: \(E^3\)-complete timelike surfaces in \(E_1^3\) are globally hyperbolic
zbMATH Open document ID: 0897.53045
author: Senchun Lin
author: Tilla Weinstein
published in: Michigan Mathematical Journal
publication date: 1998-10-20T00:00:00Z
review text: Let \(S\) be a timelike surface of Minkowski 3-space \(E^3_1\), that is, the induced metric on \(S\) is Lorentzian. First, the authors prove that \(S\) is causally stable (cf. \textit{J. K. Beem}, \textit{P. E. Ehrlich} and \textit{K. L. Easley} [`Global Lorentzian Geometry', 2nd ed. (Pure Appl. Math. 202, Marcel Dekker, New York) (1996; Zbl 0846.53001)], pp. 63-64). Then, in the case the immersion \(Z\) of \(S\) in \(E^3_1\) is supposed to be \(E^3\)-complete, the authors prove the following results: (i) \(S\) is globally hyperbolic. (ii) If \(Z\) is minimal outside a compact subset \(S_0\) of \(S\), then \(S\) is \(C^\infty\)-conformally diffeomorphic to the Lorentz plane \(E^2_1\), provided that \(S\) is simply connected.
reviewed by: Aurel Bejancu
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 1127770
zbMATH Keywords: global hyperbolicity
zbMATH Keywords: minimal immersion
zbMATH Keywords: timelike surface
zbMATH Keywords: Minkowski 3-space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029005786
OpenAlex ID: W2140480346
DOI: 10.1307/MMJ/1029005786
Recommended article: Entire timelike minimal surfaces in \(E^{3,1}\)
Recommended article: Timelike surfaces of constant mean curvature \(\pm 1\) in anti-de Sitter 3-space \(\mathbb H^3_1(-1)\)
Recommended article: On the timelike sweeping surfaces and singularities in Minkowski 3-space \(\mathbb{E}_1^3\)
Recommended article: A construction of timelike ruled surfaces in Minkowski three-space 𝔼13
Recommended article: Totally quasi-umbilic timelike surfaces in \(\mathbb{R}^{1,2}\)
Recommended article: Timelike surfaces with mean curvature one in anti-de Sitter 3-space
Recommended article: Q5173388
Recommended article: Timelike surfaces with constant mean curvature in Lorentz three-space
Recommended article: Time-like conformal homogeneous hypersurfaces with three distinct principal curvatures
Recommended article: Timelike surfaces of constant mean curvature in Minkowski 3-space
description: scientific article; zbMATH DE number 1127770