On the scalar curvature of Einstein manifolds
Copyright policy )On the scalar curvature of Einstein manifolds
We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.
LaTeX. 14 pages
- University of Göttingen Germany
- Stony Brook University United States
Mathematics - Differential Geometry, Barlow surface, Einstein metric, \(h\)-cobordism theory, Specialized structures on manifolds (spin manifolds, framed manifolds, etc.), complex Monge-Ampère equation, Mathematics - Algebraic Geometry, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Algebraic Geometry (math.AG)
Mathematics - Differential Geometry, Barlow surface, Einstein metric, \(h\)-cobordism theory, Specialized structures on manifolds (spin manifolds, framed manifolds, etc.), complex Monge-Ampère equation, Mathematics - Algebraic Geometry, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Algebraic Geometry (math.AG)
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