Helicoidal minimal surfaces in \(\mathbb H^{2} \times \mathbb R\) (Q2907029)
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scientific article; zbMATH DE number 6078022
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Helicoidal minimal surfaces in \(\mathbb H^{2} \times \mathbb R\) |
scientific article; zbMATH DE number 6078022 |
Statements
5 September 2012
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helicoidal minimal surface
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\(\mathbb H^{2} \times \mathbb R\) space
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Helicoidal minimal surfaces in \(\mathbb H^{2} \times \mathbb R\) (English)
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Screw motions in \(\mathbb H^{2} \times \mathbb R\) are rigid motions generated by rotations in \(\mathbb H^2\) and vertical translations along \(\mathbb R\). A surface in \(\mathbb H^{2} \times \mathbb R\) is called \textit{helicoidal} it it is invariant under a \(1\)-parameter group of screw motions. The authors obtain a complete description of the minimal surfaces that are helicoidal. An important result is that conjugate surfaces of the parabolic and hyperbolic helicoids in \(\mathbb H^{2} \times \mathbb R\) are certain types of catenoids.
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