A generalized Wintgen inequality for quaternionic CR-submanifolds

Abstract

The aim of this paper is to extend the classical DDVV inequality to CR-submanifolds of quaternionic Kahler manifolds of constant quaternionic sectional curvature. We first obtain a more general inequality involving the normalized scalar normal curvature $$\rho _N$$ (defined from the second fundamental form) and then derive a DDVV-type inequality involving the normalized normal scalar curvature $$\rho ^{\perp }$$ (defined from the normal curvature tensor) for CR-submanifolds in quaternionic ambient space. We also characterize the second fundamental form of those submanifolds for which the equality case holds and give a nontrivial example of submanifold satisfying the equality case identically.