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Keywords:
nonflat complex space form; real hypersurface; Hopf hypersurface; ruled real hypersurface; the tensor field $h$
nonflat complex space form; real hypersurface; Hopf hypersurface; ruled real hypersurface; the tensor field $h$
Summary:
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 $h$ $(=\frac 12 \mathcal {L}_\xi \phi )$ plays an important role in contact Riemannian geometry. In this paper, we investigate real hypersurfaces in a nonflat complex space form from the viewpoint of the parallelism of the tensor field $h$.
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