A classification of totally geodesic and totally umbilical Legendrian submanifolds of $(\kappa,\mu)$-spaces

Abstract

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.