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

This article is cited in 14 scientific papers (total in 14 papers)

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
Received: December 4, 2015
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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. M. O. Katanaev, “Chern–Simons Term in the Geometric Theory of Defects”, Phys. Rev. D, 96:8 (2017), 084054  crossref  isi  scopus
    4. M. O. Katanaev, “Normal coordinates in affine geometry”, Lobachevskii Journal of Mathematics, 39:3 (2018), 464–476  mathnet  crossref  mathscinet  isi  elib
    5. A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64  mathnet  crossref  crossref  isi  elib  elib
    6. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133  mathnet  crossref  crossref  isi  elib  elib
    7. Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81  mathnet  crossref  crossref  isi  elib  elib
    8. B. O. Volkov, “Lévy Laplacians in Hida calculus and Malliavin calculus”, Proc. Steklov Inst. Math., 301 (2018), 11–24  mathnet  crossref  crossref  isi  elib  elib
    9. N. A. Gusev, “On the definitions of boundary values of generalized solutions to an elliptic-type equation”, Proc. Steklov Inst. Math., 301 (2018), 39–43  mathnet  crossref  crossref  isi  elib  elib
    10. I. V. Volovich, V. Zh. Sakbaev, “On quantum dynamics on $C^*$-algebras”, Proc. Steklov Inst. Math., 301 (2018), 25–38  mathnet  crossref  crossref  isi  elib  elib
    11. A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271  mathnet  crossref  crossref  isi  elib  elib
    12. V. V. Zharinov, “Analysis in differential algebras and modules”, Theoret. and Math. Phys., 196:1 (2018), 939–956  mathnet  crossref  crossref  adsnasa  isi  elib
    13. M. O. Katanaev, “Description of disclinations and dislocations by the Chern–Simons action for $\mathbb{SO}(3)$ connection”, Phys. Part. Nuclei, 49:5 (2018), 890–893  crossref  isi  scopus
    14. B. O. Volkov, “Lévy Laplacians and annihilation process”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 399–409  mathnet  isi
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