Superfícies mínimas e curvatura de gauss de conóides em espaços de finsler com (α,β) - métricas
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Data
2014-03-28
Autores
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Título de Volume
Editor
Universidade Federal de Goiás
Resumo
We consider(α,β)−metric F=αφ(β
α), whereα is the euclidean metric,φ is a smooth
positive function on a symmetric interval I=(−b0,b0) and β is a 1-form with the
norm b,0
≤b<b0, on the Finsler manifoldM. We study the minimal surfaces on these
spaces with respect to the Holmes-Thompson volume form and we present the equation
that characterize the minimal hypersurfaces in general Minkowski space. We prove that
the conoids in three-dimensional space are minimal if and only if is a helicoid or a
plane, also we show that the Gauss curvature of conoid in Randers-Minkowski 3-space
is not always nonpositive on minimal surfaces. Finally, an ordinary differential equation
that characterizes minimal surfaces of revolution and an example of minimal surface of
rotationaregiven.
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Citação
DAZA, John Elber Gómez. Superfícies mínimas e curvatura de gauss de conóides em espaços de finsler com (α,β) - métricas. 2014. 85 f. Tese (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014.