Geodesic
The problem of cutting subspaces
Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 455-476

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This paper treats a natural and simply formulated problem in multidimensional geometry and linear algebra that has apparently escaped the attention of investigators. The author arrived at this problem in reflecting over a question posed by L. D. Ivanov. The greater attention is given to the geometric case of a real linear space. In this case the results are far from definitive, in contrast to the case of a linear space over the field of complex numbers. 
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     author = {M. D. Kovalev},
     title = {The problem of cutting subspaces},
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M. D. Kovalev. The problem of cutting subspaces. Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 455-476. http://geodesic.mathdoc.fr/item/SM_1994_77_2_a11/