Volumes e curvaturas médias na geometria de Finsler:superfícies mínimas
Carregando...
Data
2012-04-16
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal de Goiás
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):
Descrição
Palavras-chave
Citação
CHAVES, Newton Mayer Solorzano. Volumes e curvaturas médias na geometria de Finsler: superfícies mínimas. 2012. 75 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2012.