Ruled hypersurfaces in nonflat complex space forms with harmonic structure vector fields

Source abstract

In this paper, we prove that if the structure vector field $\xi$ of a ruled hypersurface in nonflat complex space forms is harmonic and the mean curvature is invariant along $\xi$, then the hypersurface is strongly $2$-Hopf. By applying this we construct a class of ruled hypersurfaces in a nonflat complex plane whose structure vector field is harmonic.