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 UFN, 2016, Volume 186, Number 7, Pages 763–775 (Mi ufn5498)

METHODOLOGICAL NOTES

Killing vector fields and a homogeneous isotropic universe

M. O. Katanaev

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic space–time. Although this theorem can be considered to be commonly known, its complete proof is difficult to find in the literature. An example metric is presented such that all its spatial cross sections correspond to constant-curvature spaces, but it is not homogeneous and isotropic as a whole. An equivalent definition of a homogeneous isotropic space–time in geometric terms of embedded manifolds is also given.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 The research was supported by the Russian Science Foundation (project No. 14-50-00005).

DOI: https://doi.org/10.3367/UFNr.2016.05.037808

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English version:
Physics–Uspekhi, 2016, 59:7, 689–700

Bibliographic databases:

PACS: 04.20.-q
Accepted: May 16, 2016

Citation: M. O. Katanaev, “Killing vector fields and a homogeneous isotropic universe”, UFN, 186:7 (2016), 763–775; Phys. Usp., 59:7 (2016), 689–700

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
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