{"title":"Simple closed geodesics on regular tetrahedra in spherical space","authors":"A. Borisenko, D. Sukhorebska","doi":"10.1070/SM9433","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9433","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
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.
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
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