Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 1059-1077, 2020
A certain tensor on real hypersurfaces in a nonflat complex space form
Kazuhiro Okumura
Received March 22, 2019. Published online April 14, 2020.
Abstract: 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 $h$ $(=\frac12 \mathcal{L}_\xi\phi)$ 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 $h$.
Keywords: nonflat complex space form; real hypersurface; Hopf hypersurface; ruled real hypersurface; the tensor field $h$
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Affiliations: Kazuhiro Okumura, National Institute of Technology, Asahikawa College, Shunkodai 2-2, Asahikawa 071-8142, Japan, e-mail: okumura@asahikawa-nct.ac.jp
