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In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure $(\phi ,\xi ,\eta ,g)$ induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field $h$ $(=\frac{1}{2}{ℒ}_{\xi }\phi )$ plays an important role in contact Riemannian geometry. In this paper, we...