Ricci-flat manifold
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In mathematics, Ricci-flat manifolds are Riemannian manifolds whose Ricci tensor vanishes. In physics, they are important because they represent vacuum solutions to Einstein's equations. Ricci-flat manifolds are special cases of Einstein manifolds.
Ricci-flat manifolds, in general, have restricted holonomy groups. Important cases include Calabi-Yau manifolds and hyperkähler manifolds.