Isometric deformation of \((m,n)\)-type helicoidal surface in the three dimensional Euclidean space (Q1634680)
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scientific article; zbMATH DE number 6994829
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isometric deformation of \((m,n)\)-type helicoidal surface in the three dimensional Euclidean space |
scientific article; zbMATH DE number 6994829 |
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Isometric deformation of \((m,n)\)-type helicoidal surface in the three dimensional Euclidean space (English)
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18 December 2018
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Summary: We consider a new kind of helicoidal surface for natural numbers \((m, n)\) in the three-dimensional Euclidean space. We study a helicoidal surface of value \((m, n)\), which is locally isometric to a rotational surface of value \((m, n)\). In addition, we calculate the Laplace-Beltrami operator of the rotational surface of value \((0, 1)\).
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Euclidean three-space
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helicoidal surface of value \((m,n)\)
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rotational surface of value \((m,n)\)
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mean curvature
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Gaussian curvature
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Gauss map
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0.9036782
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0.8968853
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0.88919234
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0.88873696
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0.8862615
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0.8850713
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0.88420326
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