## Abstract

If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some x ∈ X, the orbit map g → gx: G → X is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G admitting a locally faithful, orbit nonproper, isometric action on a connected Lorentz manifold. In an earlier paper, we found three collections of groups such that G admits such an action iff G is in one of the three collections. In another paper, we effectively described the first collection. In this paper, we show that the second collection contains a small, effectively described collection of groups, and, aside from those, it is contained in the union of the first and third collections. Finally, in a third paper, we effectively describe the third collection, thus solving the stated problem.

Original language | English (US) |
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Pages (from-to) | 1-45 |

Number of pages | 45 |

Journal | Geometriae Dedicata |

Volume | 98 |

Issue number | 1 |

DOIs | |

State | Published - Apr 2003 |

### Bibliographical note

Funding Information:?The author was supported in part by NSF grant DMS-9703480.

## Keywords

- Isometrics
- Lorentz manifolds
- Transformation groups