The Ruled Surfaces Generated By Quasi-Vectors in E^4 Space

Year 2023, Volume: 5 Issue: 2, 6 - 17, 30.12.2023

Aybüke Ekici Coşkun , Ziya Akça

Abstract

In this article, firstly, it is aimed to introduce the ruled surfaces, which is generated by quasi-vectors, by using the relationship between the Frenet frame and the quasi-frame, the quasi-equations, the quasi-curvatures in the spaces $\mathbb{E}^{3}$ and $\mathbb{E}^{4}$. Calculating the coefficients of
the first fundamental form, Gaussian and mean curvatures of ruled surfaces, which are generated by quasi vectors are obtained in $4$-dimensional Euclidean space. In addition to these, the relation between the Gaussian and mean curvatures of the ruled surfaces is given. Then, some geometric properties such as developability, minimality and striction line for those surfaces are investigated. Also, an example of surface curvatures by using the coefficients of fundamental form is obtained and the shapes of the ruled surface sample in projection spaces are plotted.

Keywords

Frenet frame, Quasi-frame, Ruled surface, Curvatures

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