Affiliation:
1. Fırat Üniversitesi
2. Universidad de Granada
Abstract
In this paper, we give a new approach to the rotational minimal surfaces in $4$-dimensional Euclidean space $\mathbb{R}^4$. One type of these surfaces is obtained by the composition of two families of rotations in orthogonal planes. For these surfaces, we give a new parameterization. Using this parametrization, we find new examples of rotational minimal surfaces and rotational surfaces with zero Gaussian curvature.
Publisher
International Electronic Journal of Geometry, Person (Kazim ILARSLAN)
Reference8 articles.
1. [1] Arslan, K., Bayram, B.K., Bulca, B., Öztürk, G.: Generalized rotation surfaces in E4. Results Math., 61, 315-327 (2012).
2. [2] Cole, F. N.: On rotations in space of four dimensions. Amer. J. Math. 12, 191–210 (1890).
3. [3] Dursun, U. Turgay, N.C.: Minimal and pseudo-umbilical rotational surfaces in Euclidean space E4. Mediterr. J. Math. 10, 497–506 (2013).
4. [4] Ganchev, G., Milousheva, V.: General rotational surfaces in the four-dimensional Minkowski space. Turk. J. Math. 38 (5), 883-895 (2014).
5. [5] Lee, H.: Minimal surfaces in R4 foliated by conic sections and parabolic rotations of holomorphic null curves in C4. J. Korean Math. Soc. 57, 1–19
(2020).