General Rotational Surfaces in ${\mathbb{R}}^4$ with Meridians Lying in Two-Dimensional Planes

Abstract

We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.

7 pages

References in corpus (3)

• Invariants and bonnet-type theorem for surfaces in $\r^4$
• Conformal Geometry of Surfaces in the 4-Sphere and Quaternions
• Minimal Surfaces in the Four-Dimensional Euclidean Space

Cited by in corpus (4)

• Timelike surfaces with zero mean curvature in Minkowski 4-space
• Surfaces of Revolution with Constant Gaussian Curvature in Four-Space
• General Rotational Surfaces in Pseudo-Euclidean 4-Space with Neutral Metric
• The Bi-normal fields on spacelike surfaces in ${\mathbb{R}}_1^4$