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A subset M ⊂ Rn+k is an n-dimensional submanifold of class Cp of Rn+k if, for any χ ∈ M, there exists a neighborhood U of χ in Rn+k and a C p submersion f: U → R k such that U ⊓ M = f−1 (0) (we recall tnat f is a submersion if its differential map is surjective at each point).
KeywordsVector Field Vector Bundle Open Subset Volume Form Smooth Manifold
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