Ricci curvature determines Ricci curvature tensor

Statement

Verbal statement

The Ricci curvature of a Riemannian manifold (i.e., the value of Ricci curvature tensor for unit tangent vectors) determines the Ricci curvature tensor of the manifold.

Facts used

• Ricci curvature tensor is symmetric
• Symmetric bilinear form is determined by values on same-vector pairs

Proof

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