3. Antisymmetrical tensors. External shapes

3.1 Definition

In $p \otimes E$ (respectively $p \otimes E *$ ), there is a remarkable vector subspace: that of antisymmetric tensors, which admit two equivalent definitions:

a ) that of mathematicians: a p times contravariant (respectively covariant) antisymmetric tensor is an antisymmetric multilinear form on $p$

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References

(1) - LICHNEROWICZ (A.) - Calcul tensoriel. - A. Colin (1956).
(2) - SPIVAK (M.) - Differential geometry. - Tome I. Publish or Perish.
(3) - WEYL (M.) - Temps. Espace. Matière....

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