球面空间正四面体上的简单封闭测地线

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2021-01-18 DOI:10.1070/SM9433

A. Borisenko, D. Sukhorebska

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引用次数: 3

摘要

证明了球面空间中正四面体上存在有限多条简单封闭测地线。此外，对于任意一对协素数正整数，我们找到了依赖于且满足不等式的常数，使得具有平面角的正球面四面体具有唯一的简单封闭测地线类型，直至四面体等距，而具有平面角的正球面四面体没有这样的简单封闭测地线。参考书目:19篇。

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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Simple closed geodesics on regular tetrahedra in spherical space

We prove that there are finitely many simple closed geodesics on regular tetrahedra in spherical space. Also, for any pair of coprime positive integers , we find constants and depending on and and satisfying the inequality , such that a regular spherical tetrahedron with planar angle has a unique simple closed geodesic of type , up to tetrahedron isometry, whilst a regular spherical tetrahedron with planar angle has no such geodesic. Bibliography: 19 titles.

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis