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Semi-Darboux motions of rational curves with equivalent trajectories. (English) Zbl 1050.53018

Semi-Darboux motion in complex projective space \(\mathbb P^n\) is characterized by the existence of a rational curve \(C\subset\mathbb P^n\) whose points have trajectories in a proper subspace of \(\mathbb P^n\). The author characterizes semi-Darboux motions with equivalent trajectories. The results obtained are closely related to the author’s paper [J. Geom. 73, No.1-2, 134–147 (2002; Zbl 1006.51016)].

MSC:

53A17 Differential geometric aspects in kinematics
51N15 Projective analytic geometry

Citations:

Zbl 1006.51016
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References:

[1] Darbouxsche Doppelverhältnisscharen auf Regelflächen.Österr. Akad. Wiss. Math- Natur. Kl. Sitzungsber. II198 (4-7), 159-169. · Zbl 0703.53010
[2] Rath, W., Darboux motions in threedimensional projective space, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 201, 59-87 (1992) · Zbl 0803.53012
[3] Rath, W., Matrix groups and kinematics in projective spaces, Abh. Math. Sem. Univ. Hamburg, 63, 177-196 (1993) · Zbl 0791.53014 · doi:10.1007/BF02941341
[4] Rath, W., A kinematic mapping for projective and affine motions and some applications, World Scientific, 8, 292-391 (1996) · Zbl 0956.53012
[5] H.-P. Schröcker Dievon drei projektiv gekoppelten Kegelschnitten erzeugte Ebenenmenge. PhD thesis, Technical University Graz, 2000.
[6] Schröcker, H.-P., Generatrices of rational curves, Journal of Geometry, 73, 134-147 (2002) · Zbl 1006.51016 · doi:10.1007/s00022-002-8588-2
[7] _The geometry of rational parameterized representations.Journal of Geometry (2003), accepted for publication.
[8] Vogler, H., Räumliche Zwangläufe mit ebenen Bahnkurven, Bericht d. Math, statist. Sektion des Forschungszentrums Graz, 162, 1-17 (1981) · Zbl 0472.53016
[9] Vogler, H., Zwangläufe im höchstens vierdimensionalen euklidischen RaumE^v mit affin durchlaufenen Bahnpunktsmengen, Bericht d. Math, statist. Sektion des Forschungszentrums Graz, 304, 128-143 (1989) · Zbl 0699.53011
[10] -H. Vogler, Affine Bewegungen eines Kegelschnitts mit ebenen Bahnen. Public talk in Seggauberg, July 1993.
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