Spherical 2-Dupin submanifolds
  We show that every spherical 2-Dupin submanifold that is not a hypersurface is conformally congruent to the standard embedding of the real, complex, quaternionic or octonionic projective plane. We also classify 2-CPC, 2-umbilical and weakly 2-umbilical submanifolds in space forms. 
Antonio J. Di Scala and Guilherme Machado de Freitas
math.DG