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We study Einstein metrics on smooth compact 4-manifolds with an edge-cone singularity of specified cone angle along an embedded 2-manifold. To do so, we first derive modified versions of the Gauss–Bonnet and signature theorems for arbitrary Riemannian 4-manifolds with edge-cone singularities, and then show that these yield non-trivial obstructions in the Einstein case. We then use these integra...
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ژورنال
عنوان ژورنال: Nature
سال: 1932
ISSN: 0028-0836,1476-4687
DOI: 10.1038/130952a0