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

Authors : Aybüke Ekici Coşkun, Ziya Akça

Pages : 6-17

View : 134 | Download : 182

Publication Date : 2023-12-30

Article Type : Research Paper

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