Abstract
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.
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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors are thankful to the referee for his/her careful reading and valuable suggestions which have improved this paper.
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Communicated by Mohammad Reza Koushesh.
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Yan, M., Wu, X. & Zhang, L. The Holomorphic Statistical Structures of Constant Holomorphic Sectional Curvature on Complex Space Forms. Bull. Iran. Math. Soc. 50, 17 (2024). https://doi.org/10.1007/s41980-023-00855-8
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DOI: https://doi.org/10.1007/s41980-023-00855-8