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arXiv · 1503.03803

On static three-manifolds with positive scalar curvature

L. Ambrozio
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Abstract

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.

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L. Ambrozio. 2015-03-12. On static three-manifolds with positive scalar curvature. https://arxiv.org/abs/1503.03803

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