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

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-02-27 DOI:10.1007/s41980-023-00855-8

Mingming Yan, Xinlei Wu, Liang Zhang

引用次数: 0

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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复杂空间形式上恒定全态截面曲率的全态统计结构

在本文中，我们基于维数大于 2 的复数空间形式，证明了恒定全形截面曲率的非微观统计结构的不存在性。对于二维复数空间形式，我们举例说明确实存在非微小的恒定全形截面曲率统计结构，我们还得到了这种情况下的刚性定理。最后，与复数空间形式相反，我们基于实数空间形式构建了一些新的恒定截面曲率的非微观统计结构实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.