A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3

• Autor(a) principal: Argote, Fernando Arnulfo Zuñiga
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/4550
• topic: Superfícies mínimas; Toro de Clifford; Curvatura média constante; Esfera Euclidiana S3; Ângulo de contato; Minimal surfaces; Clifford torus; Constant mean curvature; Euclidian sphere S3; Contact angle; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we refer to the study of a geometric invariant surfaces immersed in Euclidean 3-dimensional sphere S3. Such invariant, known as angle contact, is the complementary angle between the distribution of contact d and the tangent space of the surface. Montes and Verderesi [22] characterized the minimal surfaces in S3 with constant contact angle and Almeida, Brazil and Montes [4] studied some properties of immersed constant mean curvature into a round sphere S3 with constant contact angle. The our aim of this work is to deduce a general formula involving the Gaussian curvature, the mean curvature and the contact angle of surfaces immersed in Euclidean sphere 3-dimensional, which shows that the surface is flat if the contact angle is constant. Moreover, we deduce that the Clifford tori are the unique compact surfaces with constant mean curvature having such propriety. Keywords