PomeCorollary 11.15.6.A2CE95B32341 For every $e\geq 0$, there is an ample $\mu _ P$-stable bundle $E$ of rank two on $X$ with $c_1(E)=4H$ and $c_2(E)=13H^2$ that admits no smooth strongly pseudoconvex squared Finsler metric with semipositive Kobayashi curvature.
Corollary 11.15.6A2CE95B32341
Proof. By proposition 11.13.4, the two line summands of $E_0^*$ have positive degrees with respect to suitable test forms. The preceding theorem gives an ample stable bundle $E$ whose dual Dolbeault operator is as close to the split dual operator in $C^4$ as required. Apply corollary 11.12.7 to $F=E^*$. $\square$
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