Immersion (mathematics)

An injectively immersed submanifold that is not an embedding.

The Möbius strip does not immerse in codimension 0 because its tangent bundle is non-trivial.

For a closed immersion in algebraic geometry, see closed immersion.

In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective. Explicitly, f : M → N is an immersion if

is an injective function at every point p of M (where T_pX denotes the tangent space of a manifold X at a point p in X). Equivalently, f is an immersion if its derivative has constant rank equal to the dimension of M:

单词	Immersed surface
释义	Immersed surface 英语百科 Immersion (mathematics) For a closed immersion in algebraic geometry, see closed immersion. In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective. Explicitly, f : M → N is an immersion if is an injective function at every point p of M (where T_pX denotes the tangent space of a manifold X at a point p in X). Equivalently, f is an immersion if its derivative has constant rank equal to the dimension of M:
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Immersed surface

Immersion (mathematics)