A Zermelo navigation problem: Funk Metric

Authors

  • Newton Mayer Solórzano Chávez Universidade Federal da Integração Latino-Americana (UNILA), Instituto Latino-Americano de Ciências da Vida e da Natureza (ILACVN), Foz do Iguaçu, PR, Brasil https://orcid.org/0000-0001-5492-2068
  • Víctor Arturo Martínez León Universidade Federal da Integração Latino-Americana (UNILA), Instituto Latino-Americano de Ciências da Vida e da Natureza (ILACVN), Foz do Iguaçu, PR, Brasil https://orcid.org/0000-0002-2082-6665
  • Luz Gisselle Quevedo Sosa Universidade Federal da Integração Latino-Americana (UNILA), Instituto Latino-Americano de Tecnologia, Infraestrutura e Território (ILATIT), Foz do Iguaçu, PR, Brasil https://orcid.org/0000-0001-5997-8204
  • Junior Rodrigues Moyses Universidade Federal da Integração Latino-Americana(UNILA), Instituto Latino-Americano de Ciências da Vida e da Natureza (ILACVN), Foz do Iguaçu, PR, Brasil https://orcid.org/0000-0002-6754-7145

DOI:

https://doi.org/10.35819/remat2021v7i1id4574

Keywords:

Finsler Metric, Funk Metric, Navigation Problem

Abstract

The article approaches a specific model of Non-Euclidean Geometry which unitary open disk centered at the origin of the cartesian plane is endowed with a Randers metric, which models the Zermelo's navigation problem. As a result, the "Funk Geometry on the unit disk" is engendered, for which the distance is nonsymmetric. In this respect, the study presents the expressions for distance from point to point - from point to straight line, and from a straight line to point; and characterizes the circumferences in this type of geometry. Explicit examples are included.

Downloads

Download data is not yet available.

Author Biographies

  • Newton Mayer Solórzano Chávez, Universidade Federal da Integração Latino-Americana (UNILA), Instituto Latino-Americano de Ciências da Vida e da Natureza (ILACVN), Foz do Iguaçu, PR, Brasil

    http://lattes.cnpq.br/5434324704126162

  • Víctor Arturo Martínez León, Universidade Federal da Integração Latino-Americana (UNILA), Instituto Latino-Americano de Ciências da Vida e da Natureza (ILACVN), Foz do Iguaçu, PR, Brasil

    http://lattes.cnpq.br/9966158817422161

  • Luz Gisselle Quevedo Sosa, Universidade Federal da Integração Latino-Americana (UNILA), Instituto Latino-Americano de Tecnologia, Infraestrutura e Território (ILATIT), Foz do Iguaçu, PR, Brasil

    http://lattes.cnpq.br/3578145442555620

  • Junior Rodrigues Moyses, Universidade Federal da Integração Latino-Americana(UNILA), Instituto Latino-Americano de Ciências da Vida e da Natureza (ILACVN), Foz do Iguaçu, PR, Brasil

    http://lattes.cnpq.br/2207888598903867

References

CARMO, M. P. do. Geometria Diferencial de Curvas e Superfícies. 6. ed. Rio de Janeiro: SBM, 2012.

CARMO, M. P. do. Geometria Riemanniana. 5 ed. Rio de janeiro: SBM, 2011.

CHENG, X.; SHEN, Z. Finsler Geometry: An approach via Randers spaces. Beijing-Heidelberg: Science Press Beijing-Springer, 2012.

CHERN, S. S.; SHEN, Z. Riemannian-Finsler geometry. Singapore: World Scientific, 2005.

FUNK, P. Über Geometrien, bei denen die Geraden die Kürzesten sind. Mathematische Annalen, n. 101, p. 226-237, 1929.

LIMA, E. L. Análise Real. v. 1. Coleção Matemática Universitária. 12. ed. Rio de Janeiro: IMPA, 2014.

SHEN, Z. Lectures on Finsler Geometry. Singapore: World Scientific, 2001.

Downloads

Published

2021-03-29

Issue

Vol. 7 No. 1 (2021)

Section

Mathematics

License

Copyright (c) 2021 REMAT: Revista Eletrônica da Matemática

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

REMAT retains the copyright of published articles, having the right to first publication of the work, mention of first publication in the journal in other published media and distribution of parts or of the work as a whole in order to promote the magazine.

This is an open access journal, which means that all content is available free of charge, at no cost to the user or his institution. Users are permitted to read, download, copy, distribute, print, search or link the full texts of the articles, or use them for any other legal purpose, without requesting prior permission from the magazine or the author. This statement is in accordance with the BOAI definition of open access.

How to Cite

CHÁVEZ, Newton Mayer Solórzano; LEÓN, Víctor Arturo Martínez; SOSA, Luz Gisselle Quevedo; MOYSES, Junior Rodrigues. A Zermelo navigation problem: Funk Metric. REMAT: Revista Eletrônica da Matemática, Bento Gonçalves, RS, Brasil, v. 7, n. 1, p. e3010, 2021. DOI: 10.35819/remat2021v7i1id4574. Disponível em: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4574.. Acesso em: 22 nov. 2024.
Crossref
Scopus
Google Scholar
Europe PMC

Similar Articles

11-20 of 286

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)