On the surfaces of revolution with constant mean curvature in the hyperbolic space (Q1284675)
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scientific article; zbMATH DE number 1279196
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the surfaces of revolution with constant mean curvature in the hyperbolic space |
scientific article; zbMATH DE number 1279196 |
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On the surfaces of revolution with constant mean curvature in the hyperbolic space (English)
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25 May 1999
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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.
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surfaces in hyperbolic 3-space
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constant mean curvature surfaces
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hyperbolic rotational surfaces
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0.9631262
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0.95139295
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0.93837726
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0.93805265
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0.93800986
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0.93774843
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