<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>In this study, generalized rectifying ruled surfaces of Frenet-type framed base curves in the three-dimensional Euclidean space are introduced. These surfaces are a generalization of not only the tangent and binormal surfaces of Frenet-type framed base curves, but also the tangent and binormal surfaces of regular curves. Additionally, we present some geometric characterizations and properties of these surfaces. Then, the singular point classes of the surface are scrutinized and the conditions for being a cross-cap surface are stated. Moreover, generalized rectifying surfaces are examined as framed surfaces by using the framed surface theory, and we investigate the basic invariants and curvatures of them. Then, several illustrative examples with figures are given to support the theorems and results.</p>
</abstract>

In this study, generalized rectifying ruled surfaces of Frenet-type framed base curves in the three-dimensional Euclidean space are introduced. These surfaces are a generalization of not only the tangent and binormal surfaces of Frenet-type framed base curves, but also the tangent and binormal surfaces of regular curves. Additionally, we present some geometric characterizations and properties of these surfaces. Then, the singular point classes of the surface are scrutinized and the conditions for being a cross-cap surface are stated. Moreover, generalized rectifying surfaces are examined as framed surfaces by using the framed surface theory, and we investigate the basic invariants and curvatures of them. Then, several illustrative examples with figures are given to support the theorems and results.

Generalized Rectifying Ruled Surfaces of Special Singular Curves

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 Rectifying Ruled Surfaces of Special Singular Curves"}

In this study, generalized rectifying ruled surfaces of Frenet-type framed base curves in the three-dimensional Euclidean space are introduced. These surfaces...

Generalized Rectifying Ruled Surfaces of Special Singular Curves

Published Online: Oct 21, 2023

Page range: 177 - 206

Received: Sep 25, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0038

Keywords
Framed surfaces, Frenet-type framed base curves, generalized rectifying ruled surfaces

© 2023 Zehra İşbilir et al., published by Sciendo

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

Generalized Rectifying Ruled Surfaces of Special Singular Curves

Published Online: Oct 21, 2023

Page range: 177 - 206

Received: Sep 25, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0038

KeywordsFramed surfaces, Frenet-type framed base curves, generalized rectifying ruled surfaces

© 2023 Zehra İşbilir et al., published by Sciendo

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

Keywords
Framed surfaces, Frenet-type framed base curves, generalized rectifying ruled surfaces