- #1
joe2317
- 6
- 0
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])?
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.
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.