In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure ( φ, ξ, η, 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 $$h( = \frac{1}{2}{\cal L}\xi \varphi )$$ 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 .

中文翻译：

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非平坦复空间形式的真实超曲面上的某个张量

在非平坦复空间形式（即复射影空间或复双曲空间）中，实超曲面允许从环境空间引入的几乎接触的度量结构（φ, ξ, η, g ）。当然，许多几何学家已经从几乎接触度量几何的角度研究了非平坦复空间形式的真实超曲面。另一方面，众所周知，张量场 $$h( = \frac{1}{2}{\cal L}\xi \varphi )$$ 在接触黎曼几何中起着重要作用。在本文中，我们从张量场 h 的平行性的角度研究了非平坦复空间形式的真实超曲面。