Directional Tube Surface in Euclidean 4-Space

Year 2023, Volume: 5 Issue: 2, 18 - 30, 30.12.2023

Başak Yağbasan , Cumali Ekici , Hatice Tozak

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

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