Superfícies Completas com Curvatura Gaussiana Constante em H2×R e S2×R
I tiakina i:
| Kaituhi matua: | |
|---|---|
| Rā whakaputa: | 2010 |
| Hōputu: | Master thesis |
| Reo: | por |
| Puna: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tde/1969 |
Whakarāpopototanga: | 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]. |