### Abstract

A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski-Sachs-Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorized into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on a simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.

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

Pages (from-to) | 4855-4888 |

Number of pages | 34 |

Journal | Journal of Mathematical Physics |

Volume | 35 |

Issue number | 9 |

Publication status | Published - 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*35*(9), 4855-4888.

**Compact homogeneous universes.** / Koike, Tatsuhiko; Tanimoto, Masayuki; Hosoya, Akio.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 35, no. 9, pp. 4855-4888.

}

TY - JOUR

T1 - Compact homogeneous universes

AU - Koike, Tatsuhiko

AU - Tanimoto, Masayuki

AU - Hosoya, Akio

PY - 1994

Y1 - 1994

N2 - A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski-Sachs-Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorized into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on a simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.

AB - A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski-Sachs-Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorized into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on a simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.

UR - http://www.scopus.com/inward/record.url?scp=36449006639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36449006639&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36449006639

VL - 35

SP - 4855

EP - 4888

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

ER -