Superfícies Completas com Curvatura Gaussiana Constante em H2×R e S2×R
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Data
2010-03-19
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Universidade Federal de Goiás
Resumo
In this work we classify the complete surfaces with constant Gaussian curvature into the H2×R and S2×R.We show that exists a unique complete surface, up to isometries, with
positive constant Gaussian curvature into the H2×R, and greater than one, into the S2×R and that there is no complete surfaces with constant Gaussian curvature K(I) < −1 into the H2×R and S2×R. We prove that even if −1 ≤ K(I) < 0 there are infinite complete surfaces into the H2 ×R with Gaussian curvature K(I) and with additional assumption we prove there is if −1 ≤ K(I) < 0 and 0 < K(I) < 1 there is no exists complete surfaces into S2×R with Gaussian curvature K(I). These results were obtained by Aledo, Espinar and Gálvez and can be found in [1].
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CINTRA, Adriana Araujo. Complete surfaces with constant Gaussian curvature into the H2×R and S2 ×R. 2010. 99 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2010.