Superfícies mínimas com curvatura constante nas formas espaciais 4-dimensionais

• Autor(a) principal: HIEDA, Lidiane Mayumi
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000005s5c
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tde/1941
• topic: Superfícies mínimas; Curvatura constante; Imersões mínimas do 2-plano hiperbólico; Forma fundamental de tensores; Superfícies mínimas; Curvatura constante; Imersões mínimas de 2-plano hiperbólico; Forma fundamental de tensores; Minimal surfaces; Constant curvature; Minimal immersions of the hyperbolic 2-plane; Fundamental forms tensors; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This work was based on papers On Compact Minimal Surfaces with non-negative Gaussian Curvature in a Space of Constant Curvature: I and Minimal Surfaces with Constant Curvature in 4-dimensional Space Forms, by Katsuei Kenmotsu, consisting in the classification of minimal surfaces with constant Gaussian curvature K in a 4-dimensional space form without any global assumption. We will show that an isometric minimal immersion x: M2(K) → M4(c), where c is sectional curvature, is either totally geodesic, or locally Clifford Torus, or locally a Veronese surface. As a corollary, we have that there is not isometric minimal immersions with constant negative Gaussian curvature into unit sphere S4(1) even locally.