Smarandache-Based Ruled Surfaces with the Darboux Vector According to Frenet Frame in $E^3$

Year 2022, Issue: 39, 8 - 18, 30.06.2022

Süleyman Şenyurt , Davut Canlı , Elif Çan

https://doi.org/10.53570/jnt.1106331

Cited By: 1

Abstract

The paper introduces a new kind of special ruled surface. The base of each ruled surface is taken to be one of the Smarandache curves of a given curve according to Frenet frame, and the generator (ruling) is chosen to be the corresponding unit Darboux vector. The characteristics of these newly defined ruled surfaces are investigated by means of first and second fundamental forms and their corresponding curvatures. An example is provided by considering both the helix curve and the Viviani’s curve.

Keywords

Ruled surfaces, Smarandache curve, fundamental forms, curvatures, developable and minimal surfaces

Supporting Institution

None

Project Number

None

Thanks

We thank in advance to the blind reviewers for their time spent on our manuscript.

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