Classification of Möbius homogeneoussuperconformal surfaces in 𝕊5

Superconformal surfaces in space forms are characterized by the property that the curvature ellipse is a circle at every point, or equivalently, the normal vector bundle valued Hopf differential is isotropic.This paper focuses on the study of these surfaces within the framework of Mbius geometry.We construct new examples, with a particular emphasis on the case of codimension 3. We also obtain a complete classification of Mbius homogeneous superconformal surfaces in 5 .