Let <, > denote the usual scalar product on R~n given by < x, y > = ∑ from i=1 to n of x_iy_i for any x = (x_1,..., x_n) and y = (y_1,..., y_n). According to Whithney classical theorem, it is known that any manifold M can be embedded in some R~n. Suppose that i : M → R~nis an embedding of a given manifold M in R~n.
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