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 $I\le -1$. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.

14 pages