Another general inequality for CR-warped products in complex space forms

We prove that every CR-warped product NTfN⊥ in a complex space form M̄ᵐ(4c) of constant holomorphic sectional curvature 4c satisfies a general inequality: ||σ||²≥ 2p\{||∇(ln f)||²+(ln f)\}+4hpc , where h=CNT , p=RN⊥ , and σ 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.