On static three-manifolds with positive scalar curvature

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.

arXiv comment41 pages

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Cited by in corpus (6)

• Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary
• On the mass of static metrics with positive cosmological constant - I
• Uniqueness and energy bounds for static AdS metrics
• Brendle's inequality on static manifolds
• Monotonicity formulas for static metrics with non-zero cosmological constant
• Critical metrics of the volume functional on compact three-manifolds with smooth boundary