In previous papers [2, 3], B. Y. Chen introduced a Riemannian invariant δM for a Riemannian n-manifold Mⁿ. He proved in [3] that every submanifold Mⁿ in the complex hyperbolic m-space CHᵐ(-4) satisfies the sharp inequality: δM≤(n²(n-2)/2(n-1))H²-2(n+1)(n-2), where H² is the squared mean curvature. In this paper, we study Lagrangian submanifolds in CHⁿ(-4) which satisfy the equality case of the inequality.
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Chen et al. (2002) studied this question.