Scalar curvature

Let $𝑀$ be a $𝐶 𝛼$ -manifold equipped with an affine connexion $\nabla$ giving Ricci curvature $𝑅 𝑎 𝑏$ . The scalar curvature or Ricci scalar $𝑅$ is the scalar field given by the trace

𝑅 : = 𝑅 𝑎 𝑎 = 𝑔 𝑎 𝑏 𝑅 𝑎 𝑏 .

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

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