Second fundamental form of a holomorphic subbundle
= Second fundamental form of a holomorphic subbundle
{title2=$A\in\mathcal A^{1,0}(\operatorname{Hom}(S,Q))$}
For a holomorphic subbundle $S\subset E$ and quotient $Q=E/S$, the second fundamental form is $A(s)=(I-\pi_S)D_Es$. The <Leibniz rule> gives $A(fs)=fA(s)$, and holomorphicity of the subbundle makes its $(0,1)$ part vanish. Thus $A\in\mathcal A^{1,0}(\operatorname{Hom}(S,Q))$: the form factor is a <cotangent bundle>, not a tangent bundle.