Ricci curvature

Let $𝑀$ be a $𝐶 𝛼$ -manifold equipped with an affine connexion $\nabla$ giving Riemannian curvature $𝑅 𝑐 𝑑 𝑎 𝑏$ . The Ricci curvature $𝑅 𝑎 𝑏 \in T 02 (𝑀)$ is the tensor field given by the trace

𝑅 𝑎 𝑏 : = 𝑅 𝑐 𝑎 𝑐 𝑏 .

A manifold with null Ricci curvature is said to be Ricci flat.

Properties

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