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

Changping Wang and Zhenxiao Xie

Vol. 338 (2025), No. 1, 63–85
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 𝕊5.

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
Authors
Changping Wang
School of Mathematics and Statistics
Fujian Normal University
Fuzhou
China
Zhenxiao Xie
School of Mathematical Sciences
Beihang University
Beijing
China

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