On static three-manifolds with positive scalar curvature
On static three-manifolds with positive scalar curvature
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具有正标量曲率的静态三流形
DOI：
10.4310/jdg/1505268028
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
L. Ambrozio
中科院分区：
文献类型：
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作者：
L. Ambrozio
我们计算了静态三流形的Bochner型公式，并推导了在正标量曲率情况下的一些应用。我们还详细解释了与静态 n 流形的最大域相关的（黎曼）爱因斯坦 (n+1) 流形的已知一般结构，其中静态势为正。在某些例子中，这种构造不可避免地会产生沿着余维二子流形具有圆锥奇点的爱因斯坦度量。通过证明由此获得的奇异空间的爱因斯坦四流形的经典结果的版本，我们推导出具有正标量曲率的紧致静态三流形的一些分类结果。
We compute a Bochner type formula for static three-manifolds and deduce some applications in the case of positive scalar curvature. We also explain in details the known general construction of the (Riemannian) Einstein (n+1)-manifold associated to a maximal domain of a static n-manifold where the static potential is positive. There are examples where this construction inevitably produces an Einstein metric with conical singularities along a codimension-two submanifold. By proving versions of classical results for Einstein four-manifolds for the singular spaces thus obtained, we deduce some classification results for compact static three-manifolds with positive scalar curvature.