曲面上大地流的分数线性积分和中井大地四网

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2024-08-13 DOI:10.1515/advgeom-2024-0008

Sergey I. Agafonov, Thaís G. P. Alves

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引用次数: 0

摘要

我们证明，如果曲面上的大地流具有矩分数线性积分，那么这种积分的空间维度要么是 3，要么是 5，后一种情况对应于恒定高斯曲率。我们还给出了分数线性积分存在的几何标准：当且仅当表面上有一个大地4网，且与网叶相切的四个方向的交叉比恒定时，这样的积分才存在。

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Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs

We prove that if the geodesic flow on a surface has an integral which is fractional-linear in momenta, then the dimension of the space of such integrals is either 3 or 5, the latter case corresponding to constant gaussian curvature. We give also a geometric criterion for the existence of fractional-linear integrals: such an integral exists if and only if the surface carries a geodesic 4-web with constant cross-ratio of the four directions tangent to the web leaves.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.