Immersion

Definition

Let $M$ and $N$ be differential manifolds. A differentiable map $f:M\to N$ is termed an immersion at a point $m\in M$, the induced map $d{f}_m:T_{m}M\to T_{F(m)}N$ is injective.

$f$ is called an immersion if it is an immersion at every point in $M$.

We also say that $M$ is an immersed manifold in $N$.

Related notions

• Submersion, which is the same as a regular map