Real Hypersurfaces in the Complex Projective Plane Satisfying an Equality Involving $\delta(2)$

It was proved in Chen's paper [3] that every real hypersurface the complex projective plane of constant holomorphic sectional curvature $4$ satisfies $$\delta(2)\leq \frac{9}{4}H^2+5,$$ where $H$ is mean and $\delta(2)$ a $\delta$-invariant introduced by him. In this paper, we study non-Hopf hypersurfaces satisfying equality case inequality under condition along each integral curve Reeb vector field. We describe how to obtain all such hypersurfaces.