### Abstract

A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four-dimensional space-time with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the space-time isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogeneous universes. Some examples are demonstrated for Bianchi II, VI_{0}, VII_{0}, and I universal covers.

Original language | English |
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Pages (from-to) | 350-368 |

Number of pages | 19 |

Journal | Journal of Mathematical Physics |

Volume | 38 |

Issue number | 1 |

Publication status | Published - 1997 Jan |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Mathematical Physics*,

*38*(1), 350-368.

**Dynamics of compact homogeneous universes.** / Tanimoto, Masayuki; Koike, Tatsuhiko; Hosoya, Akio.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 38, no. 1, pp. 350-368.

}

TY - JOUR

T1 - Dynamics of compact homogeneous universes

AU - Tanimoto, Masayuki

AU - Koike, Tatsuhiko

AU - Hosoya, Akio

PY - 1997/1

Y1 - 1997/1

N2 - A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four-dimensional space-time with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the space-time isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogeneous universes. Some examples are demonstrated for Bianchi II, VI0, VII0, and I universal covers.

AB - A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four-dimensional space-time with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the space-time isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogeneous universes. Some examples are demonstrated for Bianchi II, VI0, VII0, and I universal covers.

UR - http://www.scopus.com/inward/record.url?scp=0031282780&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031282780&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031282780

VL - 38

SP - 350

EP - 368

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 1

ER -