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Title: Classification of projective space motions with only plane trajectories (English)
Author: Karger, Adolf
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 34
Issue: 2
Year: 1989
Pages: 133-145
Summary lang: English
Category: math
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. (English)
Keyword: projective kinematics
Keyword: special $s$-parameter motion
MSC: 53A17
MSC: 53A20
idZBL: Zbl 0678.53009
idMR: MR0990300
DOI: 10.21136/AM.1989.104341
Date available: 2008-05-20T18:36:18Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] W. Blaschke: Zur Kinematik.Abh. math. Sem. Univ. Hamburg, 22 (1958), 171-175. Zbl 0178.24302, MR 0096388, 10.1007/BF02941949
Reference: [2] J. Tölke: Eine Bemerkung zu den Projektivbewegungen mit nur ebenen Bahnkurven.Arch. der Math. 33 (1979), 279-282. MR 0559548
Reference: [3] A. Karger: Affine Darboux motions.Czechoslovak Math. Journ. 35 (110) (1985), 355-372. Zbl 0597.53004, MR 0803031


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