Growth conditions, Riemannian completeness and Lorentzian causality
type: Item
instance of: scholarly article
title: Growth conditions, Riemannian completeness and Lorentzian causality
zbMATH Open document ID: 1239.53017
published in: Journal of Geometry and Physics
publication date: 2012-03-13T00:00:00Z
review text: This elegant paper presents a study of pointwise conformal transformations of certain Riemannian metrics on the fibres and growth conditions on the corresponding conformal factors. As it is known, a conformal transformation may not always preserve the completeness of the metric. Using the growth of the conformal factor, the authors find necessary and sufficient conditions for a conformally transformed Riemannian metric to be complete. An application is found in terms of relations between the completeness of Riemannian metrics, growth conditions on conformal factors and the Cauchy hypersurface condition on the fibres of a standard stationary spacetime.
reviewed by: Raina Ivanova
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53B50
zbMATH DE Number: 6014472
zbMATH Keywords: complete Riemannian metrics
zbMATH Keywords: Finsler-Randers metrics
zbMATH Keywords: stationary spacetimes
author: A. Dirmeier
author: M. Plaue
author: M. Scherfner
MaRDI profile type: Publication
full work available at URL: j.geomphys.2011.04.017
OpenAlex ID: W2065726055
Wikidata QID: Q115353265
cites work: Q3128806
cites work: Q4871706
cites work: On the energy functional on Finsler manifolds and applications to stationary spacetimes
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cites work: Corrections to "An Analytical Criterion for the Completeness of Riemannian Manifolds"
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cites work: On the geometry of static spacetimes
cites work: Q5773759
DOI: 10.1016/J.GEOMPHYS.2011.04.017
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description: scientific article; zbMATH DE number 6014472