Detalhes bibliográficos
| Ano de defesa: |
2012 |
| Autor(a) principal: |
Chavéz, Newton Mayer Solorzano
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| Orientador(a): |
Souza, Marcelo Almeida de
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| Banca de defesa: |
Não Informado pela instituição |
| Tipo de documento: |
Dissertação
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| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Universidade Federal de Goiás
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| Programa de Pós-Graduação: |
Programa de Pós-graduação em Matemática (IME)
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| Departamento: |
Instituto de Matemática e Estatística - IME (RG)
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| País: |
Brasil
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| Palavras-chave em Português: |
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| Palavras-chave em Inglês: |
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| Área do conhecimento CNPq: |
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| Link de acesso: |
http://repositorio.bc.ufg.br/tede/handle/tde/2885
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Resumo: |
In Finsler geometry, we have several volume forms, hence various of mean curvature forms. The two best known volumes forms are the Busemann-Hausdorff and Holmes- Thompson volume form. The minimal surface with respect to these volume forms are called BH-minimal and HT-minimal surface, respectively. Let (R3; eFb) be a Minkowski space of Randers type with eFb = ea+eb; where ea is the Euclidean metric and eb = bdx3; 0 < b < 1: If a connected surface M in (R3; eFb) is minimal with respect to both volume forms Busemann-Hausdorff and Holmes-Thompson, then up to a parallel translation of R3; M is either a piece of plane or a piece of helicoid which is generated by lines screwing along the x3-axis. Furthermore it gives an explicit rotation hypersurfaces BH-minimal and HT-minimal generated by a plane curve around the axis in the direction of eb] in Minkowski (a;b)-space (Vn+1; eFb); where Vn+1 is an (n+1)-dimensional real vector space, eFb = eaf eb ea ; ea is the Euclidean metric, eb is a one form of constant length b = kebkea; eb] is the dual vector of eb with respect to ea: As an application, it give us an explicit expression of surface of rotation “ forward” BH-minimal generated by the rotation around the axis in the direction of eb] in Minkowski space of Randers type (V3; ea+eb): |
