Let U be an open set in ℝ, and let φ be a continuously differentiable function from U into the Euclidean space ℝ, where m > n. The mapping φ is called an immersion if its differential is injective at every point of U. The image of φ is called an immersed submanifold. More specifically, for m = 3, which means that the ambient Euclidean space is ℝ, the induced metric tensor is called the first fundamental form.