<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space E<sup>3</sup>. 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.</p>
</abstract>

In 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.

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

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Generalized normal ruled surface of a curve in the Euclidean 3-space"}

In 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...

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

Published Online: Aug 26, 2021

Page range: 217 - 238

Received: Aug 27, 2020

DOI: https://doi.org/10.2478/ausm-2021-0013

Keywords
normal ruled surface, minimal surface, helix, slant ruled surface

© 2021 Onur Kaya et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Aug 26, 2021

Page range: 217 - 238

Received: Aug 27, 2020

DOI: https://doi.org/10.2478/ausm-2021-0013

Keywordsnormal ruled surface, minimal surface, helix, slant ruled surface

© 2021 Onur Kaya et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
normal ruled surface, minimal surface, helix, slant ruled surface