Classification of Möbius homogeneous superconformal surfaces in $\mathbb{S}^5$

Changping Wang and Zhenxiao Xie

Vol. 338 (2025), No. 1, 63–85

DOI: 10.2140/pjm.2025.338.63

Abstract

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 Möbius geometry. We construct new examples, with a particular emphasis on the case of codimension 3. We also obtain a complete classification of Möbius homogeneous superconformal surfaces in ${\mathbb{𝕊}}^5$.

Keywords

superconformal surfaces, Möbius homogeneous surfaces, Wintgen ideal submanifolds, Möbius form

Mathematical Subject Classification

Primary: 53A05, 53A31

Milestones

Received: 24 October 2024

Revised: 6 February 2025

Accepted: 2 April 2025

Published: 20 June 2025