The Holomorphic Statistical Structures of Constant Holomorphic Sectional Curvature on Complex Space Forms

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.