| dc.creator | Mohammadpouri, Akram | es |
| dc.creator | Pashaie, Firooz | es |
| dc.date | 2017-03-23 | |
| dc.date.accessioned | 2025-10-06T15:04:53Z | |
| dc.date.available | 2025-10-06T15:04:53Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1231 | |
| dc.identifier | 10.4067/S0716-09172016000100001 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/255401 | |
| dc.description | In this paper, we study isometrically immersed hypersurfaces of the Euclidean space En+1 satisfying the condition LrH r+i = λHr+1for an integer r ( 0 ≤ r ≤ n — 1), where Hr+i 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 Hr+i 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 Hr+i = λ Hr+i 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. | es |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Universidad Católica del Norte. | en |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1231/944 | |
| dc.rights | Copyright (c) 2016 Proyecciones. Journal of Mathematics | en |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | en |
| dc.source | Proyecciones (Antofagasta); Vol. 35 No. 1 (2016); 1-10 | en |
| dc.source | Proyecciones. Revista de Matemática; Vol. 35 Núm. 1 (2016); 1-10 | es |
| dc.source | 0717-6279 | |
| dc.source | 10.22199/issn.0717-6279-2016 | |
| dc.title | On the classification of hypersurfaces in Euclidean spaces satisfying LrHr+1 = AHr+1 | es |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
