Let \(F\colon M\to N\) be a smooth map between smooth manifolds. It is a smooth immersion at a point \(p\in M\) if its differential \(dF_p\) is injective. It is called smooth immersion if it is a smooth immersion at every point in \(M\).
Remark
- If \(F\) is an immersion, then it has constant rank, in particular \[ \rank F = \dim M \]