Totally geodesic submanifolds of regular Sasakian manifolds

Abstract

Let $Q^{m+1}$ denote the family of regular Sasakian manifolds whose base manifold $M^{2m}$ is a compact symmetric space. We provide a classification of the totally geodesic submanifolds of $Q^{m+1}$ which are invariant, anti-invariant of maximal dimension or contact CR with respect to the Sasakian structure. Such submanifolds are closely related to complex and totally real totally geodesic submanifolds of the Hermitian symmetric space $M^{2m}$.