Classification of projective space motions with only plane trajectories

summary:The paper contains the solution of the classification problem for all motions in the complex projective space, which have only plane trajectories. It is shown that each such motion is a submanifold of a maximal motion with the same property. Maximal projective space motions with only plane trajectories are determined by special linear submanifolds of dimensions 2, 3, 5, 8 in $GL(4,C)$, they are denoted as $R, E_1, ..., E_6, S_1, S_2$ and given by explicit expressions