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Bochner Identity
Definition
For a smooth harmonic map u:M->N, Δ(( left bracketing bar del u right bracketing bar )^2) = ( left bracketing bar del (d u) right bracketing bar )^2 + 〈Ric_M del u, del u〉 - 〈Riem_N(u)( del u, del u) del u, del u〉, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.