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

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 t...

ver descrição completa

Detalhes bibliográficos
Autor: Argote, Fernando Arnulfo Zuñiga
Formato: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2015
País:Brasil
Recursos:Universidade Federal de Goiás (UFG)
Repositorio:Repositório Institucional da UFG
Idioma:portugués
OAI Identifier:oai:repositorio.bc.ufg.br:tede/4550
Acesso em linha:http://repositorio.bc.ufg.br/tede/handle/tede/4550
Access Level:acceso abierto
Palavra-chave: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
Descrição
Resumo: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