Surfaces with isotropic Blaschke tensor in \(S^{3}\) (Q2353247)

A surface \(M\subset S^3\) in the conformal \(3\)-sphere \(S^3\) which is free of umbilic points inherits four tensor fields that are invariant under the action of the Möbius group of \(S^3\), namely the Möbius metric \(g\), the Blaschke tensor \(A\), the Möbius second fundamental form \(B\) and the Möbius form \(\Phi\). The authors classify all surfaces for which the Blaschke tensor is isotropic, that is, there exists a smooth function \(\lambda\) so that \(A=\lambda g\).