Geometric Graph Manifolds with non-negative scalar curvature

Abstract

We classify $n$-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show 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 by showing 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.

19 pages, 3 figures. Second version with an additional corollary and improved exposition. arXiv admin note: substantial text overlap with arXiv:1611.06572

References in corpus (1)

• Manifolds with conullity at most two as graph manifolds