Manuscript XIV-C@1 · XIV-C.tex · corollary · a34d13df

Corollary: Positive conormal relation

J2: the retained characteristic configuration › A codimension-four characteristic stratum · lines 1022–1042 · proof included or linked

XIV-C@1#cor:positive

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At every point of $N^{\circ}$ , the oriented nonzero conormals

n_{R} = - \frac{d q _{R}}{2 β}, n_{1} = \frac{d q _{1}}{2 α}, n_{2} = \frac{d q _{2}}{2 ( β - α )}

satisfy $n_{R} + n_{1} + n_{2} = 0$ and reproduce (eq:nus) with $p = p_{n}$ .

There is no tangent vector $v$ at that point for which $n_{R} (v), n_{1} (v), n_{2} (v)$ are all strictly positive.

Proof. The formulas in the proof of Proposition prop:geometry give the stated covectors and sum. If all three evaluations were positive, their sum evaluated on $v$ would be positive, contradicting the zero relation.

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$n_{R} = - \frac{d q _{R}}{2 β}, n_{1} = \frac{d q _{1}}{2 α}, n_{2} = \frac{d q _{2}}{2 ( β - α )}$

Corollary: Positive conormal relation

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