Article
Full entry |
PDF
(2.1 MB)
Feedback
PDF
(2.1 MB)
Feedback
Keywords:
projective kinematics; special $s$-parameter motion
projective kinematics; special $s$-parameter motion
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.
References:
[1] W. Blaschke: Zur Kinematik. Abh. math. Sem. Univ. Hamburg, 22 (1958), 171-175. DOI 10.1007/BF02941949 | MR 0096388 | Zbl 0178.24302
[2] J. Tölke: Eine Bemerkung zu den Projektivbewegungen mit nur ebenen Bahnkurven. Arch. der Math. 33 (1979), 279-282. MR 0559548
[3] A. Karger: Affine Darboux motions. Czechoslovak Math. Journ. 35 (110) (1985), 355-372. MR 0803031 | Zbl 0597.53004
Search
Partner of
