Transitive actions on Lorentz manifolds with noncompact stabilizer

被引:4
作者
Adams, S
机构
[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
[2] Univ Henri Poincare, Fac Sci, Nancy, France
基金
美国国家科学基金会;
关键词
isometries; Lorentz manifolds; transformation groups;
D O I
10.1023/A:1024002723943
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 is an element of X, the orbit map g bar right arrow 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.
引用
收藏
页码:1 / 45
页数:45
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