PomeCorollary 11.16.4.40E5740882E3 For each $e\geq 0$, the bundle $E$ of corollary 11.15.6 can be chosen so that $E^\times $ contains a connected smooth Stein hypersurface on which the restriction of every smooth strongly pseudoconvex squared Finsler metric on $E$ has a nondegenerate critical point with at least two positive Levi eigenvalues and at most one negative Levi eigenvalue.
Corollary 11.16.440E5740882E3
Proof. The bundle constructed in the proof of theorem 11.15.5 is a fiber of an algebraic family on a chart of the prioritary stack, so it is algebraic. Apply theorem 11.16.3 with $n=r=2$, using the curvature obstruction of corollary 11.15.6. $\square$
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