I have a following problem.(adsbygoogle = window.adsbygoogle || []).push({});

Let D be an operator taking the C^oo functions F to F, and the C^oo vector fields V to V, such that D:F-->F and

D:V-->V, are linear over R(real) and

D(f Y) = f * DY+Df * Y. Here * is a multiplication

Show that D has a unique extension to an operator taking tensor fields of type(k, l) to themselves such that

(1) D is linear over R(real).

(2) D(A $ B)= DA $ B+ A $ DB. Here $ is a tensor product.

(3) for any contraction C, DC=CD.

If you have Spivak's geometry book. This is a problem 5-15.

Any help would be appreciated.

Thanks.

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# Tensor Field

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