TT-tensors and conformally flat structures on 3-manifolds
TT-tensors and conformally flat structures on 3-manifolds
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3 流形上的 TT 张量和共形平面结构
DOI：
10.4064/-41-1-109-118
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
R. Beig
中科院分区：
文献类型：
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作者：
R. Beig
研究了共形平坦三维流形$(M，g)$上的横向迹(TT)张量。线性化为$g$的Cotton-York张量将每个对称的迹张量映射为TT。关于这是否是TT条件的通解的问题，被看作是Gasqui和Goldschmidt首先发现的椭圆复形内的上同调问题，本文对此进行了综述。当$M$是单连通的且具有消失的第二个de Rham上同调时，这个问题得到了肯定的回答。
We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds $(M,g)$. The Cotton-York tensor linearized at $g$ maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. The question is answered affirmatively when $M$ is simply connected and has vanishing 2nd de Rham cohomology.