Rotational Surfaces in R⁴ with New Approaches and Examples

In this paper, we give a new approach to the rotational minimal surfaces in $4$-dimensional Euclidean space R⁴. 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.