In this paper we obtain some new characterizations of pseudo-Einstein real hypersurfaces in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$ . More precisely, we prove that a real hypersurface in $\mathbb{C}P^{2}$ or $\mathbb{C}H^{2}$ with constant mean curvature is generalized ${\mathcal{D}}$ -Einstein with constant coefficient if and only if it is pseudo-Einstein. We prove that a real hypersurface in $\mathbb{C}P^{2}$ with constant scalar curvature is generalized ${\mathcal{D}}$ -Einstein with constant coefficient if and only if it is pseudo-Einstein.

在本文中，我们获得了 $ \ mathbb {C} P ^ {2} $ 和 $ \ mathbb {C} H ^ {2} $ 中伪爱因斯坦实超曲面的一些新特征。更准确地说，我们证明了具有恒定平均曲率的 $ \ mathbb {C} P ^ {2} $ 或 $ \ mathbb {C} H ^ {2} $ 中的真实超曲面是广义的 $ {\ mathcal {D}} $ -当且仅当它是伪爱因斯坦时，系数恒定的爱因斯坦。我们证明标量曲率恒定的 $ \ mathbb {C} P ^ {2} $ 中的实际超曲面是广义的 $ {\ mathcal {D}} $ -Einstein常数，当且仅当它是伪爱因斯坦。