## Abstract

We study the Lorentzian manifolds M
_{1}
, M
_{2}
, M
_{3}
, and M
_{4}
obtained by small changes of the standard Euclidean metric on ℝ
^{4}
with the punctured origin O. The spaces M
_{1}
and M
_{4}
are closed isotropic space-time models. The manifolds M
_{3}
and M
_{4}
(respectively, M
_{1}
and M
_{2}
) are geodesically (non)complete; M
_{1}
are M
_{4}
are globally hyperbolic, while M
_{2}
and M
_{3}
are not chronological. We found the Lie algebras of isometry and homothety groups for all manifolds; the curvature, Ricci, Einstein, Weyl, and energy-momentum tensors. It is proved that M
_{1}
and M
_{4}
are conformally flat, while M
_{2}
and M
_{3}
are not conformally flat and their Weyl tensor has the first Petrov type.

Original language | English |
---|---|

Pages (from-to) | 235-248 |

Number of pages | 14 |

Journal | Siberian Mathematical Journal |

Volume | 60 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Mar 2019 |

## Keywords

- closed isotropic model
- density
- Einstein tensor
- energy-momentum tensor
- homothety group
- isometry group
- pressure
- Weyl tensor