Classification of Möbius homogenous surfaces in \({\mathbb {S}}^4\)
``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.
scientific article; zbMATH DE number 6363053