Manuscript XI-D@1 · XI-D.tex · lemma · 994a5c1b

Lemma: Dependence on the second metric coefficient

The inherited held-fixed-metric defect › Classical scalar completion · lines 938–952 · proof included or linked

XI-D@1#lem:affine

For every smooth $r$ ,

A_{2}^{sc} [H, k + r; ϕ] - A_{2}^{sc} [H, k; ϕ] = A_{1} [r; ϕ] .

Proof. The change in $X_{2}$ is $X_{1} [r]$ . The change in $ρ_{2}$ is $- E_{m}^{R} V_{1, g} [r] ϕ$ . No other displayed term depends on $k$ .

Displayed formulas in this passage

unlabeled · line 941
$A_{2}^{sc} [H, k + r; ϕ] - A_{2}^{sc} [H, k; ϕ] = A_{1} [r; ϕ] .$