Geodesic
Classification of projective space motions with only plane trajectories
Applications of Mathematics, Tome 34 (1989) no. 2, pp. 133-145
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1989.104341
Classification : 53A17, 53A20
Keywords: projective kinematics; special $s$-parameter motion 
@article{10_21136_AM_1989_104341,
     author = {Karger, Adolf},
     title = {Classification of projective space motions with only plane trajectories},
     journal = {Applications of Mathematics},
     pages = {133--145},
     year = {1989},
     volume = {34},
     number = {2},
     doi = {10.21136/AM.1989.104341},
     mrnumber = {0990300},
     zbl = {0678.53009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104341/}
}
TY  - JOUR
AU  - Karger, Adolf
TI  - Classification of projective space motions with only plane trajectories
JO  - Applications of Mathematics
PY  - 1989
SP  - 133
EP  - 145
VL  - 34
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104341/
DO  - 10.21136/AM.1989.104341
LA  - en
ID  - 10_21136_AM_1989_104341
ER  - 
%0 Journal Article
%A Karger, Adolf
%T Classification of projective space motions with only plane trajectories
%J Applications of Mathematics
%D 1989
%P 133-145
%V 34
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1989.104341/
%R 10.21136/AM.1989.104341
%G en
%F 10_21136_AM_1989_104341
Karger, Adolf. Classification of projective space motions with only plane trajectories. Applications of Mathematics, Tome 34 (1989) no. 2, pp. 133-145. doi: 10.21136/AM.1989.104341

[1] W. Blaschke: Zur Kinematik. Abh. math. Sem. Univ. Hamburg, 22 (1958), 171-175. | DOI | MR | Zbl

[2] J. Tölke: Eine Bemerkung zu den Projektivbewegungen mit nur ebenen Bahnkurven. Arch. der Math. 33 (1979), 279-282. | MR

[3] A. Karger: Affine Darboux motions. Czechoslovak Math. Journ. 35 (110) (1985), 355-372. | MR | Zbl

Cité par Sources :