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Starting from an inequality involving the invariant (D) for an anti-holomorphic submanifold of a complex space form 1 and using optimization methods on Riemannian manifolds, we establish a corresponding inequality for the invariant (D ) defined on QR-submanifolds in quaternion space forms, in terms of the squared mean curvature. We obtain a relationship between intrinsic and extrinsic invariants for QR-submanifolds of quaternion space forms.
Macsim et al. (Fri,) studied this question.
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