Surfaces with isotropic Blaschke tensor in S 3

Let M 2 be an umbilic-free surface in the unit sphere S 3. Four basic invariants of M 2 under the Moebius transformation group of S 3 are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B and Moebius form .. We call the Blaschke tensor is isotropic if there exists a smooth function . such that A = . g. In this paper, We classify all surfaces with isotropic Blaschke tensor in S 3.