Immersion

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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 df_m: T_mM \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