Möbius isotropic submanifolds in \(\mathbb{S}^n\) (Q1598957)

For an \(m\)-dimensional submanifold \((M,g)\) of the standard \(n\)-sphere \(S^n\) two Möbius invariants are introduced: A one-form \(\Phi\) called the Möbius form and a symmetric \((0,2)\)-tensor \(A\), called the Blaschke form. The submanifold is called isotropic, if \(\Phi = 0\) and \(A = \lambda g\) for a real function \(\lambda\) on \(M.\) In particular, the conformal Gauß map of an isotropic submanifold is harmonic. Then the isotropic Möbius submanifolds of \(S^n\) are classified by relating them (with the help of a fixed conformal transformation) to minimal submanifolds of the sphere, Euclidean space or hyperbolic space depending on the sign of \(\lambda.\)