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elliptic motion; projective plane motions; inflexion cubic; Darboux motions
The paper deals with one-parametric projective plane motins with the property that all points of the inflexion cubic have straight trajectories. It is shown that such motions have in the general case projective equivalent trajectories and that the inflexion cubic is in general irreducible. The cases of the above mentioned motions with reducible inflexion cubic are discussed in detail. The connection with the Darboux property is also mentioned.
[1] H. Frank: Ebene projektive Kinematik. Dissertation Univ. Karlsruhe, 1968.
[2] J. Tölke: Ebene projektive Kinematik I. II, III. Math. Nachr. 63 (1974) 167-185, 187-196; 68 (1975) 221-237. DOI 10.1002/mana.3210630114 | MR 0365376
[3] A. Karger: Affine Darboux motions. Czech. Math. Journ., in print. Zbl 0597.53004
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