Einstein metrics, complex surfaces, and symplectic 4-manifolds
نویسنده
چکیده
Which smooth compact 4-manifolds admit an Einstein metric with non-negative Einstein constant? A complete answer is provided in the special case of 4-manifolds that also happen to admit either a complex structure or a symplectic structure. A Riemannian manifold (M, g) is said to be Einstein if it has constant Ricci curvature, in the sense that the function v −→ r(v, v) on the unit tangent bundle {v ∈ T M| ‖v‖g = 1} is constant, where r denotes the Ricci tensor of g. This is of course equivalent to demanding that g satisfy the Einstein equation
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