A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3
Data
2015-02-27
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Universidade Federal de Goiás
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.
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Citação
ARGOTE, F. A. Z. A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3. 2015. 78 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2015.