We prove that the structure Jacobi operator $R_{\xi }$ on a real hypersurface M in the complex projective space $\mathbb{C}{P}^2$ satisfies $R_{\xi }+\kappa {\varphi }^2=0$ with $\kappa \in {\mathbb{R}}^{⁎}$ (or equivalently, constant Reeb sectional curvature) if and only if either M is of type (A) or M is locally congruent to a non-homogeneous Hopf hypersurface with vanishing Hopf principal curvature.

中文翻译：

---

真正的超曲面 $\mathbb{C}{P}^2$ 里氏截面曲率恒定

我们证明了Jacobi算子的结构 ${\mathrm{[R}}_{\xi }$在复射影空间中的实超曲面M上$\mathbb{C}{P}^2$ 满足 ${\mathrm{[R}}_{\xi }+\kappa {\varphi }^2=0$ 与 $\kappa \in {\mathbb{[R}}^{⁎}$（或等效地，恒定的Reeb截面曲率），且仅当M为（A）类型或M在局部上与Hopf主曲率消失的非均匀Hopf超曲面一致时。