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Results tagged with tensor-calculus
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user 320425
Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.
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The dual of a surface element in 4-space
So you do have $df_{ij}=dx_i dx'_j-dx_j dx'_i$. If the indexpair $i,j$ is contracted with an indexpair of another antisymmetric object like $\epsilon^{ijkl}$ one can replace $dx_i dx'_j-dx_j dx'_i$ by …
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