Directional Tube Surface in Euclidean 4-Space

Authors : Başak Yağbasan, Cumali Eki̇ci̇, Hatice Tozak

Pages : 18-30

View : 97 | Download : 155

Publication Date : 2023-12-30

Article Type : Research Paper

Abstract :The aim of this paper is to study characterization of tube surfaces (called directional tube surfaces) with respect to the q-frame in Euclidean $4$-space $\\mathbb{E}^{4}$. First, a parametrization of these directional tube surfaces in $\\mathbb{E}^{4}$ is established. Then, the normals of the directional tube surfaces, denoted as $\\mathbf{U}_{1}$ and $\\mathbf{U}_{2}$, are determined respectively. Furthermore, the Gaussian curvature $K$ and the mean curvature $H$ of the directional tube surfaces are investigated. Subsequently, an example of a directional tube surface is given in $\\mathbb{E}^{4}$, together with visual representations of this tube surfaces in projection space.
Keywords : quasi frame, curvatures, Euclidean space, Tube surface