Minimal surfaces of rotation in Finsler space with a Randers metric |
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Authors: | Marcelo Souza Keti Tenenblat |
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Institution: | (1) Instituto de Matemática e Estatística, Universidade Federal de Goiás, 74001-970, Goiania, GO, Brazil (e-mail: msouza@mat.ufg.br), BR;(2) Departamento de Matemática, Universidade de Brasília, 70910-900, Brasília, DF, Brazil (e-mail: keti@mat.unb.br), BR |
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Abstract: | We consider Finsler spaces with a Randers metric F=α+β, on the three dimensional real vector space, where α is the Euclidean metric and β=bdx
3
is a 1-form with norm b,0≤b<1. By using the notion of mean curvature for immersions in Finsler spaces introduced by Z. Shen, we get the ordinary differential
equation that characterizes the minimal surfaces of rotation around the x
3
axis. We prove that for every b,0≤b<1, there exists, up to homothety, a unique forward complete minimal surface of rotation. The surface is embedded, symmetric
with respect to a plane perpendicular to the rotation axis and it is generated by a concave plane curve. Moreover, for every
there are non complete minimal surfaces of rotation, which include explicit minimal cones.
Received: 30 November 2001 / Published online: 10 February 2003
RID="⋆"
ID="⋆" Partially supported by CAPES
RID="⋆⋆"
ID="⋆⋆" Partially supported by CNPq and PROCAD. |
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