 Curvature commutator on a contravariant tensor

ID: curvature-commutator-on-a-contravariant-tensor

For a type-

(2, 0)

tensor, the Ricci identity acts once on each contravariant index:

[\nabla_{α}, \nabla_{β}] T^{μν} = R^{μ}_{ρ α β} T^{ρ ν} + R^{ν}_{ρ α β} T^{μ ρ} .

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