Manuscript IX-E-3@1 · IX-E-3.tex · lemma · 8c41417a

Lemma: Injectivity of the surface coefficient

Derivative support and surface non-cancellation · lines 467–478 · proof included or linked

If $n$ is non-null, the map $v \mapsto B (v)$ is injective.

Proof. Contract (eq:Bsurface) with $n_{α}$ :

n_{α} B^{α β} (v) = - \frac{1}{2} (n_{α} n^{α}) v^{β} .

Thus $B (v) = 0$ implies $v = 0$ .

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