Isotropic submanifolds in a Euclidean space (Q1819753)

In this paper the following theorem is proved. Let M be an m-dimensional Riemannian manifold isotropically immersed in \(E^ n\). If the Gauss map \(\Gamma\) is conformal and the image \(\Gamma\) (M) is totally umbilical in the Grassmann manifold G(m,n-m), then M is a minimal and isotropic submanifold in a hypersphere \(S^{n-1}\) of \(E^ n\) with parallel second fundamental form.