| 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:
|
http://hdl.handle.net/10338.dmlcz/104341 |
| . |
| 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 |
| . |
