Let \(\phi\colon M\to N\) be a smooth map between two smooth manifolds. A regular level set is a level set \(\mathcal{L}=\phi^{-1}(\{c\})\) such that for every point \(p\in \mathcal{L}\) the differential \(d\phi_p\colon T_pM\to T_{\phi(p)}N\) is surjective (such points and the value \(c\) are also called regular).
Examples
Remark
- every regular level set is an embedded submanifold . In this case \(\phi\) is called defining map for the regular level set. [@lee2013smooth_manifolds, Corollary 5.14]