| dc.creator | Mohammadpouri, Akram | |
| dc.creator | Pashaie, Firooz | |
| dc.date | 2017-03-23 | |
| dc.identifier | http://www.revistaproyecciones.cl/article/view/1231 | |
| dc.identifier | 10.4067/S0716-09172016000100001 | |
| 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+iis 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-ES |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Universidad Católica del Norte. | es-ES |
| dc.relation | http://www.revistaproyecciones.cl/article/view/1231/944 | |
| dc.rights | Derechos de autor 2016 Proyecciones. Journal of Mathematics | es-ES |
| dc.source | Proyecciones. Journal of Mathematics; Vol 35 No 1 (2016); 1-10 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 35 Núm. 1 (2016); 1-10 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.title | On the classification of hypersurfaces in Euclidean spaces satisfying LrHr+1 = AHr+1 | es-ES |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Artículo revisado por pares | es-ES |
