ELA, Volume 8, pp. 60-82, May 2001, abstract.

Natural group actions on tensor products of 
three real vector spaces with finitely many orbits

Dragomir Z. Djokovic and Peter W. Tingley
 
Let G be the direct product of the general linear groups 
of three real vector spaces U, V, W of finite dimensions 
l, m, n (2 <= l <= m <= n). Consider the natural action 
of G on the tensor product of these spaces. The number of 
G-orbits in X is finite if and only if l=2 and m=2 or 3. 
In these cases the G-orbits and their connected components 
are classified, and the closure of each of the components 
is determined. The proofs make use of recent results of 
P.G. Parfenov, who solved the same problem for complex 
vector spaces.