Einstein metrics and smooth structures
Copyright policy )Einstein metrics and smooth structures
We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4-manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4-manifolds with two smooth structures which admit Einstein metrics with opposite signs of the scalar curvature.
10 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper1.abs.html
- University of Basel Switzerland
Surfaces of general type, Mathematics - Differential Geometry, Applications of global analysis to structures on manifolds, 57R55, 57R57, 53C25, 14J29, non-diffeomorphic, Einstein metric, Geometric Topology (math.GT), 53C25, Topology of the Euclidean \(4\)-space, \(4\)-manifolds, Mathematics - Geometric Topology, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), 57R55, 4-manifolds, Differentiable structures in differential topology, FOS: Mathematics, 57R57, smooth structure, 4–manifold, 14J29
Surfaces of general type, Mathematics - Differential Geometry, Applications of global analysis to structures on manifolds, 57R55, 57R57, 53C25, 14J29, non-diffeomorphic, Einstein metric, Geometric Topology (math.GT), 53C25, Topology of the Euclidean \(4\)-space, \(4\)-manifolds, Mathematics - Geometric Topology, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), 57R55, 4-manifolds, Differentiable structures in differential topology, FOS: Mathematics, 57R57, smooth structure, 4–manifold, 14J29
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