The Sasakian statistical structures of constant ϕ-sectional curvature on Sasakian space forms

IF 0.6 4区 数学 Q3 MATHEMATICS
Xinlei Wu, Yanyan Sheng, Liang Zhang
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引用次数: 0

Abstract

In this paper, we investigate the Sasakian statistical structures of constant ϕ-sectional curvature based on Sasakian space forms. We obtain the classification of this kind of Sasakian statistical structures. Our classification results show that the Sasakian statistical structures of constant ϕ-sectional curvature on a Sasakian space form with dimension higher than 3 must be almost-trivial; on a 3-dimensional Sasakian space form, in addition to the almost-trivial Sasakian statistical structure, there exist other Sasakian statistical structures which satisfy the constant ϕ-sectional curvature condition. We also point out that a rigidity result for cosymplectic statistical structures of constant ϕ-sectional curvature on 3-dimensional cosymplectic space forms in [11] can be improved to the corresponding classification result.

萨萨基空间形式上恒定ϕ截面曲率的萨萨基统计结构
本文以萨萨空间形式为基础,研究了恒定ϕ截面曲率的萨萨统计结构。我们获得了这类 Sasakian 统计结构的分类。我们的分类结果表明,在维数大于 3 的 Sasakian 空间形式上的ϕ截面曲率恒定的 Sasakian 统计结构必须是几乎三维的;在三维 Sasakian 空间形式上,除了几乎三维的 Sasakian 统计结构之外,还存在其他满足ϕ截面曲率恒定条件的 Sasakian 统计结构。我们还指出,[11]中关于三维折射空间形式上恒定ϕ截面曲率的折射统计结构的刚度结果可以改进为相应的分类结果。
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来源期刊
CiteScore
1.00
自引率
20.00%
发文量
81
审稿时长
6-12 weeks
期刊介绍: Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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