We study ruled real hypersurfaces whose shape operators have constant squared norm in nonflat complex space forms. In particular, we prove the nonexistence of such hypersurfaces in the projective case. We also show that biharmonic ruled real hypersurfaces in nonflat complex space forms are minimal, which provides their classification due to a known result of Lohnherr and Reckziegel.

中文翻译：

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非平坦复空间形式中规则超曲面的若干问题

我们研究了规则的实超曲面，其形状算子在非平坦复杂空间形式中具有恒定的平方范数。特别是，我们证明了在投影情况下不存在这种超曲面。我们还表明，非平坦复杂空间形式中的双调和规则实超曲面是最小的，由于 Lohnherr 和 Reckziegel 的已知结果，这提供了它们的分类。