Submersions, level sets

[kellertuer]

It might sometimes be useful for embedded manifolds to work in the embedding and consider the level set function $h(\iota(p)) = 0$, where $\iota(p)$ is the embed function. This is closely related to submersions.
For both the derivative would be useful, for example to constrain $\text{Ker} Dh(p) = 0$ in the embedding, when trying to find a tangent vector (using constraints).

What would be the best way to name these (cf. a first idea also at #734)

• $h$ could be level_set(M,q) for any q from the embedding of M?
• $Dh$ would need a nice name
• submersions would probably need two manifolds (Domain and range)?