A δ -Invariant for QR-Submanifolds in Quaternion Space Forms

Abstract

Starting from an inequality involving the invariant δ(D) for an anti-holomorphic submanifold ofa complex space form [1] and using optimization methods on Riemannian manifolds, we establisha corresponding inequality for the invariant δ(D ⊥ ) defined on QR-submanifolds in quaternionspace forms, in terms of the squared mean curvature. We obtain a relationship between intrinsicand extrinsic invariants for QR-submanifolds of quaternion space forms.