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September 2017 On static three-manifolds with positive scalar curvature
Lucas Ambrozio
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J. Differential Geom. 107(1): 1-45 (September 2017). DOI: 10.4310/jdg/1505268028


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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Lucas Ambrozio. "On static three-manifolds with positive scalar curvature." J. Differential Geom. 107 (1) 1 - 45, September 2017.


Received: 24 May 2015; Published: September 2017
First available in Project Euclid: 13 September 2017

zbMATH: 1385.53020
MathSciNet: MR3698233
Digital Object Identifier: 10.4310/jdg/1505268028

Rights: Copyright © 2017 Lehigh University


Vol.107 • No. 1 • September 2017
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