Generic Submanifolds of Quaternion Kaehler Manifolds and Wintgen Type Inequality

Abstract

We define and study generic submanifolds of a quaternion Kaehler manifolds, give examples and obtain integrability conditions for distributions and investigate the geometry of their leaves. Further, we investigate the main properties of both, totally umbilical and totally geodesic generic submanifolds and we study mixed foliate generic submanifolds. Finally, we obtain generalized Wintgen type inequality for generic submanifolds in a quaternionic space form.