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.

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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.

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Published

2021-03-29

Issue

Vol. 7 No. 1 (2021)

Section

Mathematics

License

Copyright (c) 2021 REMAT: Revista Eletrônica da Matemática

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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.
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