3 problems

Identify $\mathbb{R}^4$ with the quaternion skew field $\mathbb{H}$. Let an analytic surface in $\mathbb{R}^4$ have two noncospheric circular arcs through every point, fully contai…

An analytic surface in $\mathbb{R}^3$ is the image of an injective real analytic map from a planar domain with nondegenerate differential at every point. Two circular arcs are tran…

The examples under consideration include Euclidean translational surfaces, Clifford translational surfaces, Darboux cyclides, and their images under Möbius transformations. A surfa…