Let $X$ and $Y$ be complex manifolds of dimensions $n$ and $r$, and let $i:Y\hookrightarrow X$ be a holomorphic embedding. Let $T_X$ and $T_Y$ denote their holomorphic tangent bundles, let $di:T_Y\to i^*T_X$ be the holomorphic bundle morphism induced by the differential of $i$, and let $N_{Y/X}$ denote the holomorphic normal bundle, locally identified with the quotient of $i^*T_X$ by $di(T_Y)$. Then there is a short exact sequence of holomorphic vector bundles on $Y$,

\begin{align*} 0 \longrightarrow T_Y \xrightarrow{\,di\,} i^*T_X \xrightarrow{\,q\,} N_{Y/X} \longrightarrow 0, \end{align*}

where $q$ is the quotient morphism.