Bounded distance geodesic foliations in Riemannian planes

A conjecture of Burns and Knieper (1991) asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature,...

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Detalles Bibliográficos
Autores: Ge, Jian, Guijarro Santamaría, Luis
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/741820
Acceso en línea:https://hdl.handle.net/10486/741820
https://dx.doi.org/10.1515/crelle-2023-0023
Access Level:acceso abierto
Palabra clave:Riemaannian plane
geodesic foliation
conjugate points
Burns-Knieper conjeture
Matemáticas
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spelling Bounded distance geodesic foliations in Riemannian planesGe, JianGuijarro Santamaría, LuisRiemaannian planegeodesic foliationconjugate pointsBurns-Knieper conjetureMatemáticasA conjecture of Burns and Knieper (1991) asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature, and under the hypothesis of visibility at some point. Along the way, we show that all geodesic line foliations on a Riemannian 2-plane must be homeomorphic to the standard oneThe first author was partially supported by National Key R&D Program of China grant 2020YFA0712800 and the Fundamental Research Funds for the Central Universities. The second author was supported in part by research grants MTM2017-85934-C3-2-P from the Ministerio de Economía y Competitividad de España (MINECO), PID2021-124195NB-C32 from the Ministerio de Ciencia e Innovación (MICINN), and by ICMAT Severo Ochoa project CEX2019-000904-S (MINECO)De Gruyter BrillDepartamento de MatemáticasFacultad de CienciasGobierno de España20232023-05-01research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10486/741820https://dx.doi.org/10.1515/crelle-2023-0023reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7418202026-06-23T12:46:27Z
dc.title.none.fl_str_mv Bounded distance geodesic foliations in Riemannian planes
title Bounded distance geodesic foliations in Riemannian planes
spellingShingle Bounded distance geodesic foliations in Riemannian planes
Ge, Jian
Riemaannian plane
geodesic foliation
conjugate points
Burns-Knieper conjeture
Matemáticas
title_short Bounded distance geodesic foliations in Riemannian planes
title_full Bounded distance geodesic foliations in Riemannian planes
title_fullStr Bounded distance geodesic foliations in Riemannian planes
title_full_unstemmed Bounded distance geodesic foliations in Riemannian planes
title_sort Bounded distance geodesic foliations in Riemannian planes
dc.creator.none.fl_str_mv Ge, Jian
Guijarro Santamaría, Luis
author Ge, Jian
author_facet Ge, Jian
Guijarro Santamaría, Luis
author_role author
author2 Guijarro Santamaría, Luis
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
Gobierno de España
dc.subject.none.fl_str_mv Riemaannian plane
geodesic foliation
conjugate points
Burns-Knieper conjeture
Matemáticas
topic Riemaannian plane
geodesic foliation
conjugate points
Burns-Knieper conjeture
Matemáticas
description A conjecture of Burns and Knieper (1991) asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature, and under the hypothesis of visibility at some point. Along the way, we show that all geodesic line foliations on a Riemannian 2-plane must be homeomorphic to the standard one
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-05-01
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10486/741820
https://dx.doi.org/10.1515/crelle-2023-0023
url https://hdl.handle.net/10486/741820
https://dx.doi.org/10.1515/crelle-2023-0023
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv De Gruyter Brill
publisher.none.fl_str_mv De Gruyter Brill
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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