Classification of Möbius homogenous surfaces in \({\mathbb {S}}^4\)
type: Item
instance of: scholarly article
title: Classification of Möbius homogenous surfaces in \({\mathbb {S}}^4\)
zbMATH Open document ID: 1314.53024
author: Zhenxiao Xie
author: Changping Wang
published in: Annals of Global Analysis and Geometry
publication date: 2014-10-31T00:00:00Z
review text: ``A surface \(M^2\) in \({\mathbb {S}}^4\) is called Möbius homogeneous if for any two points \(p,\, q \in M\) there exists a Möbius transformation which takes \( p\) to \(q\) and keeps \(M^2\) invariant''. In this work the authors give a complete classification of the Möbius homogeneous surfaces in \({\mathbb {S}}^4,\) continuing previous papers on this topic [\textit{T. Li} et al., Ark. Mat. 51, No. 2, 315--328 (2013; Zbl 1291.53010); \textit{R. Sulanke}, Colloq. Math. Soc. János Bolyai 46, 1141--1154 (1988; Zbl 0643.53014); \textit{C. Wang}, Manuscr. Math. 96, No. 4, 517--534 (1998; Zbl 0912.53012); Nagoya Math. J. 139, 1--20 (1995; Zbl 0863.53034)], especially of the first author. Their method consist in choosing the well-defined Möbius invariant frame with the aim to simplify the structure equations as linear differential equations with constant coefficients and then to resolve them more easily.
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53A55
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 6363053
zbMATH Keywords: moduli space
zbMATH Keywords: Möbius invariant
zbMATH Keywords: conformal Gauss map
zbMATH Keywords: Möbius homogeneous surface
MaRDI profile type: Publication
full work available at URL: s10455-014-9421-5
OpenAlex ID: W2085694364
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DOI: 10.1007/S10455-014-9421-5
description: scientific article; zbMATH DE number 6363053