Projected Chern connection
= Projected Chern connection
{title2=$D_S=\pi_SD_E$}
If $S$ is a holomorphic subbundle of a <Hermitian vector bundle> $E$, its induced <Chern connection> is $D_S=\pi_SD_E$ on sections of $S$. <Orthogonal projection> preserves <metric compatibility>, and holomorphicity of $S$ preserves the required $(0,1)$ operator. Uniqueness of the <Chern connection> therefore identifies the projected connection.