Abstract
The aim of this paper is to extend the classical DDVV inequality to CR-submanifolds of quaternionic Kähler manifolds of constant quaternionic sectional curvature. We first obtain a more general inequality involving the normalized scalar normal curvature
ρ
N
(defined from the second fundamental form) and then derive a DDVV-type inequality involving the normalized normal scalar curvature
ρ
⊥
(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.