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](http://arxiv.org/abs/math/0508428) and P. Baier's PhD thesis [available here](http://people.maths.ox.ac.uk/hitchin/hitchinstudents/baier.ps.gz). 


I found this by Cohen and Helminik *Trilinear alternating forms on a vector space of dimension $7$* [available here](http://oai.cwi.nl/oai/asset/1725/1725A.pdf) but I was wondering if it is possible to find in literature the real case explicitly done.



Classification of 3-forms in dimension 7
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.


