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

Abstract

We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of (κ, µ)-spaces with Boeckx invariant I ≤ −1. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.2010 Mathematics Subject Classification. 53C15, 53C25, 53C40.