Manuscript XII-D@1 · XII-D.tex · section · 308a2080

The finite cubic identity and its sign

D5: the exact signed plateau variation › The finite cubic identity and its sign · lines 1080–1097

For a contravariant rank-two density define

(L_{ξ}^{dens} v)^{μν} = ξ^{ρ} \partial_{ρ} v^{μν} - v^{ρ ν} \partial_{ρ} ξ^{μ} - v^{μ ρ} \partial_{ρ} ξ^{ν} + (\partial_{ρ} ξ^{ρ}) v^{μν} .

Set

s_{ξ} [γ] = L_{ξ} γ + \frac{1}{2} L_{ξ} K ξ .

This tensor is compactly supported in $U$ .

Displayed formulas in this passage

unlabeled · line 1083
$(L_{ξ}^{dens} v)^{μν} = ξ^{ρ} \partial_{ρ} v^{μν} - v^{ρ ν} \partial_{ρ} ξ^{μ} - v^{μ ρ} \partial_{ρ} ξ^{ν} + (\partial_{ρ} ξ^{ρ}) v^{μν} .$
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$s_{ξ} [γ] = L_{ξ} γ + \frac{1}{2} L_{ξ} K ξ .$