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Classification of projective space motions with only plane trajectories

Adolf Karger (1989)

Aplikace matematiky

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 G L ( 4 , C ) , they are denoted as R , E 1 , . . . , E 6 , S 1 , S 2 and given by explicit expressions.

Discrete Laplace cycles of period four

Hans-Peter Schröcker (2012)

Open Mathematics

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction.

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