In this paper, we prove the non-existence of non-trivial statistical structures of constant holomorphic sectional curvature based on complex space forms with dimension greater than 2. For 2-dimensional complex space forms we show an example to illustrate there do exist non-trivial statistical structures of constant holomorphic sectional curvature, and we also obtain a rigidity theorem in this case. Finally, in contrast to complex space forms, we construct some new examples of non-trivial statistical structures of constant sectional curvature based on real space forms.

中文翻译：

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复空间形式上常全纯截面曲率的全纯统计结构

在本文中，我们证明了基于维数大于2的复空间形式的常全纯截面曲率的非平凡统计结构的不存在性。对于二维复空间形式，我们举一个例子来说明确实存在非-恒定全纯截面曲率的平凡统计结构，在这种情况下我们还得到了刚性定理。最后，与复杂的空间形式相比，我们构造了一些基于真实空间形式的恒定截面曲率的非平凡统计结构的新例子。