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Tensor Fields as Multilinear Maps by arthikko is a document available to read on EtoBox.

1) There is a 1-to-1 correspondence between tensor fields and multilinear maps of vector fields and covector fields. A tensor field can be represented as a multilinear map, and vice versa. 2) Given a tensor field A, its corresponding multilinear map Ȧ is defined by Ȧ(X1, ..., Xk, ω1, ..., ωl)(p) = Ap(X1p, ..., Xlp, ω1p, ..., ωlp). 3) Given a multilinear map A, the corresponding tensor field is constructed by defining Ap(v1, ..., vk, w1, ..., wl) = A(X1

Author

arthikko

Language

EN