A ruled real hypersurface in a complex space form is a real hypersurface having a codimension one foliation by totally geodesic complex hyperplanes of the ambient space. Our main purpose of this paper is to introduce a new viewpoint to investigate such hypersurfaces in complex hyperbolic space $$\mathbb {CH}^n$$ CH n . As an application, we study minimal ruled real hypersurfaces in $$\mathbb {CH}^n$$ CH n and also those having constant scalar curvature.

中文翻译：

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复双曲空间中规则实超曲面的新构造及其应用

复空间形式的规则实超曲面是具有由环境空间的全测地复超平面构成的共维一叶理的实超曲面。我们这篇论文的主要目的是引入一个新的观点来研究复杂双曲空间 $$\mathbb {CH}^n$$ CH n 中的这种超曲面。作为一个应用，我们研究了 $$\mathbb {CH}^n$$ CH n 中的最小规则实超曲面以及那些具有恒定标量曲率的超曲面。