Let Y[tex]_{1}[/tex],..,Y[tex]_{k}[/tex] be vector fields and let A be a tensor field of type [tex]^{k}_{1}[/tex]. Could you explain how applying k contractions to A[tex]\otimes[/tex]Y[tex]_{1}[/tex][tex]\otimes[/tex]...Y[tex]_{k}[/tex] yields A(Y[tex]_{1}[/tex]...Y[tex]_{k}[/tex])?(adsbygoogle = window.adsbygoogle || []).push({});

Actually, could you first explain why contraction of w[tex]\otimes[/tex]Y is equal to w(Y)?

Here, w is a 1-form and Y is a vector field.

Thank you.

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# Contraction of a tensor

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