Surfaces with isotropic Blaschke tensor in S 3

Let M² be an umbilic-free surface in the unit sphere S³. Four basic invariants of M² under the Moebius transformation group of S³ are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B and Moebius form Φ. We call the Blaschke tensor is isotropic if there exists a smooth function λ such that A = λg. In this paper, We classify all surfaces with isotropic Blaschke tensor in S³.