# Classification of projective space motions with only plane trajectories

Aplikace matematiky (1989)

- Volume: 34, Issue: 2, page 133-145
- ISSN: 0862-7940

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topKarger, Adolf. "Classification of projective space motions with only plane trajectories." Aplikace matematiky 34.2 (1989): 133-145. <http://eudml.org/doc/15570>.

@article{Karger1989,

abstract = {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.},

author = {Karger, Adolf},

journal = {Aplikace matematiky},

keywords = {projective kinematics; special $s$-parameter motion; projective kinematics; special s-parameter motion},

language = {eng},

number = {2},

pages = {133-145},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Classification of projective space motions with only plane trajectories},

url = {http://eudml.org/doc/15570},

volume = {34},

year = {1989},

}

TY - JOUR

AU - Karger, Adolf

TI - Classification of projective space motions with only plane trajectories

JO - Aplikace matematiky

PY - 1989

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 34

IS - 2

SP - 133

EP - 145

AB - 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.

LA - eng

KW - projective kinematics; special $s$-parameter motion; projective kinematics; special s-parameter motion

UR - http://eudml.org/doc/15570

ER -

## References

top- W. Blaschke, 10.1007/BF02941949, Abh. math. Sem. Univ. Hamburg, 22 (1958), 171-175. (1958) Zbl0178.24302MR0096388DOI10.1007/BF02941949
- J. Tölke, Eine Bemerkung zu den Projektivbewegungen mit nur ebenen Bahnkurven, Arch. der Math. 33 (1979), 279-282. (1979) MR0559548
- A. Karger, Affine Darboux motions, Czechoslovak Math. Journ. 35 (110) (1985), 355-372. (1985) Zbl0597.53004MR0803031

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