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I'm looking for a classification of $3$-forms over a real vector space of dimension $7$ as for the $3$-forms in dimension $6$. References on the latter case are R. Bryant On the geometry of almost complex $6$-manifolds available here and P. Baier's PhD thesis available here.

I found this by Cohen and Helminik Trilinear alternating forms on a vector space of dimension $7$ available here but I was wondering if it is possible to find in literature the real case explicitly done.

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The paper

Djoković, Dragomir Ž.(1983). Classification of trivectors of an eight-dimensional real vector space, Linear and Multilinear Algebra, 13: 1, 3 — 39

gives a systematic classification of 3-forms over a real vector space of dimension 8, including the classification of 3-forms over a real vector space of dimension 7.

Djoković attributes the first classification of 3-forms over a real vector space of dimension 7 (by ad-hoc methods) to Westwick:

R. Westwick. Real trivectors of rank seven, Linear and Multilinear Algebra 10 (1981), 183-204.

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