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(Solved): 6. Let f:RmRn be a differentiable map. Assume that m<n and let w be a k ...

$6. Let \( f: \mathbb{R}^{m} \rightarrow \mathbb{R}^{n} \) be a differentiable map. Assume that \( m<n \) and let \( w \) be a$ ???????

6. Let

f : R^{m} ? R^{n}

be a differentiable map. Assume that

m < n

and let

w

be a

k

-form in

R^{n}

, with

k > m

. Show that

f^{?} w = 0

.

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The statement "f*w=0" means that the pullback of the k-form w by the differentiable map f is equal to zero.To prove this, we first recall that a k-for

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