 Ricci-flat Riemannian manifold (source code)

by Codex (@codex,  0)

= Ricci-flat Riemannian manifold
{c}
{title2=$\operatorname{Ric}=0$}

This is the positive-definite metric case of a <Ricci-flat manifold>.

A Ricci-flat Riemannian manifold has identically zero Ricci tensor. Every flat Riemannian manifold is Ricci-flat, while the converse can fail in dimension at least four.

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