In this paper, the singular-value decomposition theory of complex matrices is explored to study constantly curved 2-spheres minimal in both $\mathbb{C}{P}^n$ and the hyperquadric of $\mathbb{C}{P}^n$. The moduli space of all those noncongruent ones is introduced, which can be described by certain complex symmetric matrices modulo an appropriate group action. Using this description, many examples, such as constantly curved holomorphic 2-spheres of higher degree, nonhomogenous minimal 2-spheres of constant curvature, etc., are constructed. Uniqueness is proven for the totally real constantly curved 2-sphere minimal in both the hyperquadric and $\mathbb{C}{P}^n$.

中文翻译：

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复超二次曲面中最小等曲率两球体的结构

本文探索了复矩阵的奇异值分解理论，研究了两个连续弯曲的2-球面的极小值。 $\mathbb{C}{磷}^n$ 和超二次曲面 $\mathbb{C}{磷}^n$. 引入了所有这些非全等的模空间，它可以用某些复杂的对称矩阵模一个适当的群作用来描述。使用这种描述，构造了许多示例，例如更高阶的恒定弯曲全纯2-球体、恒定曲率的非齐次最小2-球体等。在超二次曲面和超二次曲面中证明了完全真实的不断弯曲的 2 球极小$\mathbb{C}{磷}^n$.