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Ricci-flat manifold
In
mathematics
,
Ricci-flat manifolds
are
Riemannian manifolds
whose
Ricci curvature
vanishes. In
physics
, they represent
vacuum solutions
to the analogues of
Einstein's equations
for Riemannian manifolds of any dimension, with vanishing
cosmological constant
. Ricci-flat manifolds are special cases of
Einstein manifolds
, where the cosmological constant need not vanish.
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