= Curvature formula for a holomorphic subbundle
{title2=$\Theta_F=(\Theta_E)_{11}-B\wedge\overline B^t$}
In an adapted smooth unitary frame with input-index connection convention, the <Chern connection> matrix has blocks $(\theta_F,B;-\overline B^t,\theta_Q)$, where the <second fundamental form of a holomorphic subbundle> $B$ has type $(1,0)$. The <Cartan curvature equation with input indices> gives the displayed formula. If the ambient curvature is zero, $\Theta_F(X,\overline X)=-B(X)B(X)^\dagger$ is negative semidefinite. Dualizing the <determinant line bundle> therefore gives semipositive curvature.
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