Geodesic
Generatrix of catenoid of space 3-form
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 1, pp. 81-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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Constant mean curvature surfaces of revolution in euclidean 3-space are known as surfaces of Ch. Delaunay. They possess one remarkable property: their profile curves (generatrices) are the trajectories of focuses of conic sections by its rolling along the straight line. Analogous construction is realized in the space forms $H^3$ and $S^3$ in the case of minimal surfaces of revolution and the following theorem is proved. Theorem. Generatrix of catenoid of revolution of space form $H^3(S^3)$ is the trajectory of focus of hyperbolic (spherical) parabola by its rolling along the geodesic ray. 
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     author = {L. A. Masaltsev},
     title = {Generatrix of catenoid of space 3-form},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
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L. A. Masaltsev. Generatrix of catenoid of space 3-form. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 1, pp. 81-99. http://geodesic.mathdoc.fr/item/JMAG_1999_6_1_a5/