JP Journal of Geometry and Topology
Volume 2, Issue 2, Pages 141 - 147
(July 2002)
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SOME PROPERTIES OF THE HELICOID AS RULED SURFACES
Dae Won Yoon (Korea)
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Abstract:
In this paper, we study some properties related to the second Gaussian curvature of ruled surfaces in a 3-dimensional Euclidean space. Furthermore, we characterize ruled surfaces in a 3-dimensional Euclidean space in terms of the second Gaussian curvature, the mean curvature and the Gaussian curvature. In particular, we show that the only ruled surface with vanishing second Gaussian curvature is a helicoid. |
| Keywords and phrases: helicoid, minimal surface, ruled surface, second Gaussian curvature, mean curvature, Gaussian curvature. |
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