Geodesic
Projective plane motions with infinitely many straight trajectories
Applications of Mathematics, Tome 30 (1985) no. 1, pp. 36-49
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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.
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.
DOI : 10.21136/AM.1985.104125
Classification : 53A17
Keywords: elliptic motion; projective plane motions; inflexion cubic; Darboux motions 
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Karger, Adolf. Projective plane motions with infinitely many straight trajectories. Applications of Mathematics, Tome 30 (1985) no. 1, pp. 36-49. doi: 10.21136/AM.1985.104125

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[3] A. Karger: Affine Darboux motions. Czech. Math. Journ., in print. | Zbl

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