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.
Birincil Dil | İngilizce |
---|---|
Konular | Cebirsel ve Diferansiyel Geometri |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 30 Aralık 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 5 Sayı: 2 |