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We prove that every CR-warped product Nₓ₅N_ in a complex space form M^m (4c) of constant holomorphic sectional curvature 4c satisfies a general inequality: ||||^2 2p\|| (f) ||^{2+ (f) \}+4hpc, where h=₂Nₓ, p=ₑN, and is the second fundamental form. We also completely classify CR-warped products in a complex space form which satisfy the equality case of this inequality.
Bang‐Yen Chen (2003) studied this question.