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Displaying similar documents to “Affine space motions with only plane trajectories”

Classification of projective space motions with only plane trajectories

Adolf Karger (1989)

Aplikace matematiky

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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.

Euclidean space motions with affinely equivalent trajectories

Adolf Karger (1983)

Aplikace matematiky

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The author studies the Euclidean space motions with the property that the trajectory of every point is an affine image of a given space curve. Such motions split into plane motions and translations and their trajectories are cylindrical curves. They are characterized as motions with the following property: Not all trajectories are plane curves and if any trajectory has a planar point, it lies in a plane. Motions with infinitely many straight trajectories form a special subclass of those...