| Journal: | Proyecciones (Antofagasta) |
| Database: | PERIÓDICA |
| System number: | 000405929 |
| ISSN: | 0716-0917 |
| Authors: | Mohammadpouri, Akram1 Pashaie, Firooz2 |
| Institutions: | 1University of Tabriz, Faculty of Mathematical Sciences, Tabriz. Irán 2University of Maragheh, Faculty of Basic Sciences, Maragheh. Irán |
| Year: | 2016 |
| Season: | Mar |
| Volumen: | 35 |
| Number: | 1 |
| Pages: | 1-10 |
| Country: | Chile |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Analítico |
| English abstract | In this paper, we study isometrically immersed hypersurfaces of the Euclidean space En+1 satisfying the condition Lr −→H r+1 = λ −→H r+1 for an integer r ( 0 ≤ r ≤ n − 1), where −→H r+1 is the (r + 1)th mean curvature vector field on the hypersurface, Lr is the linearized operator of the first variation of the (r + 1)th mean curvature of hypersurface arising from its normal variations. Having assumed that on a hypersurface x : Mn → En+1, the vector field −→H r+1 be an eigenvector of the operator Lr with a constant real eigenvalue λ, we show that, Mn has to be an Lr-biharmonic, Lr-1-type, or Lr-null-2- type hypersurface. Furthermore, we study the above condition on a well-known family of hypersurfaces, named the weakly convex hypersurfaces (i.e. on which principal curvatures are nonnegative). We prove that, any weakly convex Euclidean hypersurface satisfying the condition Lr −→H r+1 = λ −→H r+1 for an integer r ( 0 ≤ r ≤ n − 1), has constant mean curvature of order (r + 1). As an interesting result, we have that, the Lr-biharmonicity condition on the weakly convex Euclidean hypersurfaces implies the r-minimality |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas puras, Geometría diferencial, Hipersuperficies, Subvariedades, Inmersiones, Espacios euclideanos |
| Keyword: | Mathematics, Pure mathematics, Differential geometry, Hypersurfaces, Submanifolds, Immersions, Euclidean spaces |
| Full text: | Texto completo (Ver PDF) |
