Gronwall关于具有两个铅笔线的3-ebs的猜想

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-10-13 DOI:10.1016/j.difgeo.2023.102071

Sergey I. Agafonov

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引用次数: 0

摘要

我们在线性三腹板的特殊情况下证明了古老的Gronwall猜想，其2个叶理是2铅笔线。对于非六边形三腹板，我们还引入了一个投影无扭Cartan连接族，该族的每个成员的腹板叶都是测地线，并给出了一个腹板线性化准则。

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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Gronwall's conjecture for 3-webs with two pencils of lines

We prove the old-standing Gronwall conjecture in the particular case of linear 3-webs whose 2 foliations are 2 pencils of lines. For a non-hexagonal 3-web, we also introduce a family of projective torsion-free Cartan connections, the web leaves being geodesics for each member of the family, and give a web linearization criterion.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

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.