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

<p>In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces.</p>
</abstract>

In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces.

Generalized Helicoidal Surfaces in Euclidean 5-space

Kırıkkale University, Faculty of Sciences and Arts

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Generalized Helicoidal Surfaces in Euclidean 5-space"}

In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal...

Generalized Helicoidal Surfaces in Euclidean 5-space

Published Online: Nov 23, 2021

Page range: 269 - 283

Received: Mar 03, 2021

Accepted: Apr 28, 2021

DOI: https://doi.org/10.2478/auom-2021-0044

Keywords
Helicoidal surface, minimal surface, flat surface, normal curvature tensor, complete surface

© 2021 Ali Uçum et al., published by Sciendo

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

Generalized Helicoidal Surfaces in Euclidean 5-space

Published Online: Nov 23, 2021

Page range: 269 - 283

Received: Mar 03, 2021

Accepted: Apr 28, 2021

DOI: https://doi.org/10.2478/auom-2021-0044

KeywordsHelicoidal surface, minimal surface, flat surface, normal curvature tensor, complete surface

© 2021 Ali Uçum et al., published by Sciendo

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

Keywords
Helicoidal surface, minimal surface, flat surface, normal curvature tensor, complete surface