Let $M$ and $N$ be smooth manifolds with $\dim M = m$ and $\dim N = n$, and let $F:M\to N$ be a smooth submersion. For each $q\in N$, the fiber $F^{-1}(\{q\})$, equipped with the [subspace topology](/page/Subspace%20Topology) from $M$, has a natural embedded submanifold structure of dimension $m-n$. If $F^{-1}(\{q\})=\varnothing$, this is understood as the empty [smooth manifold](/page/Smooth%20Manifold) of dimension $m-n$. For every $p\in F^{-1}(\{q\})$, the tangent space of the embedded submanifold satisfies

\begin{align*} T_p(F^{-1}(\{q\}))=\ker(dF_p)\subset T_pM. \end{align*}