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On static three-manifolds with positive scalar curvature
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Ambrozio, Lucas (2017) On static three-manifolds with positive scalar curvature. Journal of Differential Geometry, 107 (1). pp. 1-45. doi:10.4310/jdg/1505268028 ISSN 0022-040X.
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Official URL: http://dx.doi.org/10.4310/jdg/1505268028
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.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Scalar field theory, Geometry, Differential, Bochner technique, Three-manifolds (Topology) | ||||||
Journal or Publication Title: | Journal of Differential Geometry | ||||||
Publisher: | Lehigh University | ||||||
ISSN: | 0022-040X | ||||||
Official Date: | 13 September 2017 | ||||||
Dates: |
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Volume: | 107 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 1-45 | ||||||
DOI: | 10.4310/jdg/1505268028 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 30 October 2019 | ||||||
Date of first compliant Open Access: | 30 October 2019 | ||||||
RIOXX Funder/Project Grant: |
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