Superfícies mínimas e curvatura de gauss de conóides em espaços de finsler com (α,β) - métricas

• Autor(a) principal: Daza, John Elber Gómez
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/3634
• topic: Imersão isométrica; Subvariedade mínima; Conóides; Curvaturade Gauss; Isometrical immersion; Minimal submanifold; Conoids; Gauss Curvature; ALGEBRA::GEOMETRIA ALGEBRICA

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.