A classification of totally geodesic and totally umbilical Legendrian   submanifolds of $(\kappa,\mu)$-spaces
  We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of $(\kappa,\mu)$-spaces with Boeckx invariant $I \leq -1$. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct. 
Alfonso Carriazo, Ver\'onica Mart\'in-Molina, Luc Vrancken
math.DG