On bijections of Lorentz manifolds, which leave the class of spacelike paths invariant
type: Item
instance of: scholarly article
title: On bijections of Lorentz manifolds, which leave the class of spacelike paths invariant
zbMATH Open document ID: 0586.53025
DOI: 10.1016/0166-8641(85)90033-1
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: The main purpose of this paper is to prove the following theorem: Let f be a bijection between Lorentzian manifolds such that f and \(f^{-1}\) preserve space-like paths. Then f is a homeomorphism with respect to the manifold topologies. Furthermore using results of \textit{D. B. Malament} [J. Math. Phys. 18, 1399-1404 (1977; Zbl 0355.53033)] it is shown that an S-homeomorphism (i.e. a homeomorphism with respect to the space topologies [see \textit{R. Göbel}, Mitt. Math. Ges. Hamb. 10, 763-771 (1980; Zbl 0571.53041)]) between time-orientable Lorentz manifolds is a conformal diffeomorphism.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 83C40
zbMATH DE Number: 3940166
zbMATH Keywords: space-like paths
zbMATH Keywords: homeomorphism
zbMATH Keywords: S-homeomorphism
zbMATH Keywords: space topologies
zbMATH Keywords: conformal diffeomorphism
author: Rudolf Z. Domiaty
reviewed by: Bernd Wegner
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90033-1
OpenAlex ID: W2013527587
cites work: Topologies for Lorentz manifolds: The space topology
cites work: The smooth-path topology for curved space–time which incorporates the conformal structure and analytic Feynman tracks
cites work: Q3689054
cites work: Isometric embeddings of Riemannian and pseudo-Riemannian manifolds.
cites work: The Large Scale Structure of Space-Time
cites work: A new topology for curved space–time which incorporates the causal, differential, and conformal structures
cites work: Q5341405
cites work: Q3911050
cites work: Q3851306
cites work: The class of continuous timelike curves determines the topology of spacetime
cites work: Weaker Versions of Zeeman's Conjectures on Topologies for Minkowski Space
cites work: The topology of Minkowski space
description: scientific article; zbMATH DE number 3940166