Rotational Surfaces in $\mathbb R^4$ with New Approaches and Examples

Year 2024, Volume: 17 Issue: 1, 97 - 105, 23.04.2024

Muhittin Evren Aydın , Lopez Rafael

https://doi.org/10.36890/iejg.1430210

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.

Keywords

Rotational surface, minimal surface, Gauss curvature

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