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Schröcker, H.-P.

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

Abh. Math. Semin. Univ. Hamb. 73, 271-279 (2003).
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)].
Reviewer: Victor Alexandrov (Novosibirsk)

MSC:

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

Keywords:

projective kinematics; rational curve; Darboux motion; rational parameterized equation; semi-kinematic mapping kernel completion; kernel independent set

Citations:

Zbl 1006.51016
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\textit{H. P. Schröcker}, Abh. Math. Semin. Univ. Hamb. 73, 271--279 (2003; Zbl 1050.53018)
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References:

[1] Darbouxsche Doppelverhältnisscharen auf Regelflächen.Österr. Akad. Wiss. Math- Natur. Kl. Sitzungsber. II 198 (4–7), 159–169.
[2] W. Rath, Darboux motions in threedimensional projective space.Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 201 (1992), 59–87. · Zbl 0803.53012
[3] –, Matrix groups and kinematics in projective spaces.Abh. Math. Sem. Univ. Hamburg 63 (1993), 177–196. · Zbl 0791.53014
[4] –, A kinematic mapping for projective and affine motions and some applications. In: F. Dillen, B. Komrakov, U. Simon, I. Van de Woestijne and L. Verstraelen (eds),Geometry and Topology of Submanifolds, Vol. 8, World Scientific, 1996, pp. 292–391. · Zbl 0956.53012
[5] H.-P. Schröcker Dievon drei projektiv gekoppelten Kegelschnitten erzeugte Ebenenmenge. PhD thesis, Technical University Graz, 2000.
[6] – Generatrices of rational curves.Journal of Geometry 73 (2002), 134–147. · Zbl 1006.51016
[7] _ The geometry of rational parameterized representations.Journal of Geometry (2003), accepted for publication.
[8] H. Vogler, Räumliche Zwangläufe mit ebenen Bahnkurven.Bericht d. Math, statist. Sektion des Forschungszentrums Graz 162 (1981), 1–17.
[9] –, Zwangläufe im höchstens vierdimensionalen euklidischen RaumE v mit affin durchlaufenen Bahnpunktsmengen,Bericht d. Math, statist. Sektion des Forschungszentrums Graz 304 (1989), 128–143.
[10] -H. Vogler, Affine Bewegungen eines Kegelschnitts mit ebenen Bahnen. Public talk in Seggauberg, July 1993.
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