We classify $n$-dimensional geometric graph manifolds with non-negative scalar curvature by first showing that if $n>3$, the universal cover splits off a codimension 3-Euclidean factor. We then proceed with the classification of the 3-dimensional case, where the condition is equivalent to the eigenvalues of the Ricci tensor being $(\lambda ,\lambda ,0)$ with $\lambda ⩾0$. In this case we prove that such a manifold is either a lens space or a prism manifold with a very rigid metric. This allows us to also classify the moduli space of such metrics: it has infinitely many connected components for lens spaces, while it is connected for prism manifolds.

中文翻译：

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具有非负标量曲率的几何图形流形

我们分类 $n$具有非负标量曲率的维几何图流形首先证明如果 $n>3$，通用覆盖分裂出一个余维 3-欧几里得因子。然后我们继续对 3 维情况进行分类，其中条件等价于 Ricci 张量的特征值是$(\lambda ,\lambda ,0)$ 和 $\lambda ⩾0$. 在这种情况下，我们证明这样的流形要么是透镜空间，要么是具有非常严格的度量的棱镜流形。这使我们还可以对此类度量的模空间进行分类：它具有无限多个用于透镜空间的连通分量，而对于棱镜流形则是连通的。