The vector Laplacian can be generalized to yield the tensor Laplacian (A_(μν;λ))^(;λ) | = | (g^λκ A_(μν;λ))_(;κ) | = | g^λκ (d^2 A_μν)/(dx^λ dx^κ) - g^μν Γ^λ_μν (dA_μν)/(dx^λ) | = | 1/sqrt(g) d/(dx^ν)(sqrt(g)g^μν (dA_μν)/(dx^μ)) | = | 1/sqrt(g) d/(dx^μ)(sqrt(g)g^μκ (dA_μν)/(dx^κ)) | = | 1/sqrt(g) (sqrt(g)g^μκ A_(μν, κ))_(, μ), where g_(;κ) is a covariant derivative, g_μν is the metric tensor, g = det(g_μν), A_(μν, κ) is the comma derivative, and

Laplacian | vector Laplacian

Pierre-Simon Laplace