Índice e estabilidade de hipersuperfícies mínimas e de curvatura média constante na esfera
The aim of this work is to study the index either of compact minimal or constant mean curvature hypersurfaces immersed into the Euclidean unit sphere Sn+1. The main ingredient to do that is the Jacobi operator which appears on the second formula of variation of area. On the minimal case we shall pre...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | Brasil |
| Institución: | Universidade Federal do Ceará (UFC) |
| Repositorio: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/61580 |
| Acceso en línea: | http://www.repositorio.ufc.br/handle/riufc/61580 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria diferencial Curvatura média |
| Sumario: | The aim of this work is to study the index either of compact minimal or constant mean curvature hypersurfaces immersed into the Euclidean unit sphere Sn+1. The main ingredient to do that is the Jacobi operator which appears on the second formula of variation of area. On the minimal case we shall present low estimative for the index and we shall show that the minimal Clifford tori are the unique minimal hypersurfaces over which a = -2n , where a stands for the first eigenvalue of the Jacobi operator. Moreover, it is easy to see that totally umbilical sphere Sn (r) em Sn+1 , with 0 < r < 1, are weakly stable. Finally we shall show that the index is bigger that or equal to n+2 for compact constant mean curvature hypersurfaces of Sn+1 provides they have constant scalar curvature. Moreover , Clifford tori Sk (r) x Sn-k (1 - r2)½ attain such index provided (k/n + 2 )½ ≤ r ≤ (k + 2/n + 2) ½. |
|---|