Properiy disconunuous isometric group actions on innomogeneous Lorentzian manifolds
Properiy disconunuous isometric group actions on innomogeneous Lorentzian manifolds
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非均匀洛伦兹流形上的固有不协等距群作用
DOI：
10.1007/s10711-013-9834-5
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Jun-ichi Mukuno
中科院分区：
文献类型：
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作者：
加藤 諒;川元 祐奈;下村 克己;Jun-ichi Mukuno
如果齐次空间的子群通过左作用适当地不连续地作用于它，则称这个商空间为Clifford-Klein形式。Calabi和Markus(Ann Math(2)75：63-76,1962)证明了Lorentz群中不存在左作用在De Sitter空间上真不连续的无限子群。由此推论，De Sitter空间的紧致Clifford-Klein形式永远不存在。本文利用微分几何的技巧，将E.Calabi和L.Markus的定理推广到一类不一定齐次的洛伦兹流形上。
If a homogeneous spaceis acted properly discontinuously upon by a subgroupofvia the left action, the quotient spaceis called aClifford–Klein form. In Calabi and Markus (Ann Math (2) 75: 63–76, 1962) proved that there is no infinite subgroup of the Lorentz groupwhose left action on the de Sitter spaceis properly discontinuous. It follows that a compact Clifford–Klein form of the de Sitter space never exists. In the present paper, we provide a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous by using the techniques of differential geometry.