On pedal curves of normal surfaces of biharmonic curves in \(\widetilde{{\mathcal{SL}}_2(\mathbb R)}\) (Q6486673)
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scientific article; zbMATH DE number 6369844
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On pedal curves of normal surfaces of biharmonic curves in \(\widetilde{{\mathcal{SL}}_2(\mathbb R)}\) |
scientific article; zbMATH DE number 6369844 |
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On pedal curves of normal surfaces of biharmonic curves in \(\widetilde{{\mathcal{SL}}_2(\mathbb R)}\) (English)
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14 November 2014
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The authors give necessary and sufficient conditions for a curve in \(\widetilde{\mathrm{SL}_2(R)}\) to be biharmonic, in terms of its curvatures and obtain its parameter equation. They consider the normal ruled surface over biharmonic curve and its pedal curve. In particular, they find the explicit parameter equation of the corresponding pedal curve and give some illustrations.
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normal ruled surface
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