## On the surfaces of revolution with constant mean curvature in the hyperbolic space. (Sur les surfaces de révolution à courbure moyenne constante dans l’espace hyperbolique.)(French)Zbl 0921.53029

The meridians of a Euclidean surface of revolution with constant mean curvature have a nice kinematic generation. This paper shows that in hyperbolic three-space there exists a hyperbolic kinematics counterpart. The author studies plane curves $$\gamma _{e,p}$$ which share some focal properties with the Euclidean conic sections. The path of its focus under the plane hyperbolic rolling of $$\gamma$$ on a geodesic $$a$$ shall be denoted by $$c$$. Hyperbolic rotation of $$c$$ around the axis $$a$$ gives a hyperbolic surface of revolution with meridian $$c$$. This surface then has constant (hyperbolic) mean curvature.
Reviewer: O.Röschel (Graz)

### MSC:

 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53A35 Non-Euclidean differential geometry
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### References:

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