Levi-Civita tensor

to see


since we are requiring “canonical” duality, i.e.  covectors, \varepsilon^k:V\to R, do


one uses

\varepsilon^i\!\wedge\!\varepsilon^j\!\wedge\!\varepsilon^k\!\wedge\!\varepsilon^l\!=\!\!\sum_{\sigma\in S_4}\!(\!-1\!)^{\sigma}\!\varepsilon^{\sigma(i)}\!\otimes\!\varepsilon^{\sigma(j)}\!\otimes\!\varepsilon^{\sigma(k)}\!\otimes\!\varepsilon^{\sigma(l)}


Filed under differential geometry, fiber bundle, geometry, multilinear algebra

2 responses to “Levi-Civita tensor

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