Weakly $\phi$-invariant real hypersurfaces of dimension three

In this paper, it is proved that a real hypersurface of dimension three in a nonflat complex space form is weakly $\phi$-invariant if and only if it is locally congruent to a type $(A)$ hypersurface, or a ruled hypersurface or a type of strongly $2$-Hopf hypersurfaces whose local structures are determined completely by a system of ordinary differential equations.