Local Normal Form for Submersions

Theorem

Let $\Omega\subset\R^n$ be open.

Let $f : \Omega \to \R^k$ be an submersion.

Let $p\in\Omega$.

Then $n\geq k$, and there exists a local diffeomorphism $\phi$ around $f(p)$ such that

$\phi\circ f (x, y) = x$ for all $(x, y)$ in a neighborhood of $p$.

Proof

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Also see

• Local Normal Form for Immersions