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Generalized normal ruled surface of a curve in the Euclidean 3-space

Generalized normal ruled surface of a curve in the Euclidean 3-space AbstractIn this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space E3. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal (equivalently, helicoid). We examine the conditions for the curves lying on this surface to be asymptotic curves, geodesics or lines of curvature. Finally, we obtain the Frenet vectors of generalized normal ruled surface and get some relations with helices and slant ruled surfaces and we give some examples for the obtained results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Universitatis Sapientiae, Mathematica de Gruyter

Generalized normal ruled surface of a curve in the Euclidean 3-space

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References (17)

Publisher
de Gruyter
Copyright
© 2021 Onur Kaya et al., published by Sciendo
eISSN
2066-7752
DOI
10.2478/ausm-2021-0013
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space E3. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal (equivalently, helicoid). We examine the conditions for the curves lying on this surface to be asymptotic curves, geodesics or lines of curvature. Finally, we obtain the Frenet vectors of generalized normal ruled surface and get some relations with helices and slant ruled surfaces and we give some examples for the obtained results.

Journal

Acta Universitatis Sapientiae, Mathematicade Gruyter

Published: Aug 1, 2021

Keywords: normal ruled surface; minimal surface; helix; slant ruled surface; 53A05; 53A25

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