Abstract
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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
.
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Keywords
superconformal surfaces, Möbius homogeneous surfaces,
Wintgen ideal submanifolds, Möbius form
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Mathematical Subject Classification
Primary: 53A05, 53A31
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Milestones
Received: 24 October 2024
Revised: 6 February 2025
Accepted: 2 April 2025
Published: 20 June 2025
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© 2025 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
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