On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics

We study a class of two-dimensional Finsler metrics defined by a Riemannian metric α and a 1-form β. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact that β is always closed for those metrics in higher dime...

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Detalles Bibliográficos
Autor principal: Yang, Guojun
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3819927/
https://www.ncbi.nlm.nih.gov/pubmed/24250263
http://dx.doi.org/10.1155/2013/291491
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author Yang, Guojun
author_facet Yang, Guojun
author_sort Yang, Guojun
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description We study a class of two-dimensional Finsler metrics defined by a Riemannian metric α and a 1-form β. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact that β is always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of two-dimensional (α, β)-metrics which are Douglasian, and some families of examples are given for projectively flat classes with β being not closed.
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spelling pubmed-38199272013-11-18 On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics Yang, Guojun ScientificWorldJournal Research Article We study a class of two-dimensional Finsler metrics defined by a Riemannian metric α and a 1-form β. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In particular, it shows that the known fact that β is always closed for those metrics in higher dimensions is no longer true in two-dimensional case. Further, we determine the local structures of two-dimensional (α, β)-metrics which are Douglasian, and some families of examples are given for projectively flat classes with β being not closed. Hindawi Publishing Corporation 2013-10-22 /pmc/articles/PMC3819927/ /pubmed/24250263 http://dx.doi.org/10.1155/2013/291491 Text en Copyright © 2013 Guojun Yang. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Yang, Guojun
On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics
title On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics
title_full On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics
title_fullStr On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics
title_full_unstemmed On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics
title_short On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics
title_sort on a class of two-dimensional douglas and projectively flat finsler metrics
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3819927/
https://www.ncbi.nlm.nih.gov/pubmed/24250263
http://dx.doi.org/10.1155/2013/291491
work_keys_str_mv AT yangguojun onaclassoftwodimensionaldouglasandprojectivelyflatfinslermetrics

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