Generic QR-submanifolds of quaternion Kaehler manifolds

Abstract

In this article, generic QR-submanifolds of a quaternion Kaehler manifold are introduced as a generalization of QR-submanifolds and real hypersurfaces of a quaternion Kaehler manifold. Examples of such submanifolds are given, the geometry of the distributions on the submanifold is examined, and mixed geodesic generic QR-submanifolds, a special kind of geodesicity, are investigated. Finally, the main properties of totally umbilical and totally geodesic generic QR-submanifolds are explored.