Superfícies Completas com Curvatura Gaussiana Constante em H2×R e S2×R
Saved in:
| Main Author: | |
|---|---|
| Publication Date: | 2010 |
| Format: | Master thesis |
| Language: | por |
| Source: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tde/1969 |
Summary: | 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]. |
Be the first to leave a comment!