On a class of submanifolds carrying an extrinsic totally umbilical foliation

In this paper we give a conformal classification of all euclidean submanifo lds carrying a parallel principal curvature normal under the intrinsic addi tional assumption that the associated conformal conullity is involutive and the leaves are extrinsic spheres in the submanifold in the sense of Nomizu . We also provide several applications of this result.