Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1

Abstract: In this paper, we try to give a classification of spacelike hypersurfaces of the Lorentz-Minkowski space-time E 1 n+1 , whose mean curvature vector field of order (k+ 1) is an eigenvector of the kth linearized operator L k , for a non-negative integer k less than n. The operator L k is...

Description complète

Enregistré dans:

Détails bibliographiques
Auteur principal:	Pashaie,Firooz
Langue:	English
Publié:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Sujets:	Spacelike hypersurfaces Lk-biharmonic k-maximal Weakly convex
Accès en ligne:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300711
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

id	oai:scielo:S0716-09172021000300711
record_format	dspace
spelling	oai:scielo:S0716-091720210003007112021-06-07Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1Pashaie,Firooz Spacelike hypersurfaces Lk-biharmonic k-maximal Weakly convex Abstract: In this paper, we try to give a classification of spacelike hypersurfaces of the Lorentz-Minkowski space-time E 1 n+1 , whose mean curvature vector field of order (k+ 1) is an eigenvector of the kth linearized operator L k , for a non-negative integer k less than n. The operator L k is defined as the linear part of the first variation of the (k + 1)th mean curvature of a hypersurface arising from its normal variations. We show that any spacelike hypersurface of E 1 n+1 satisfying the condition L k H k+1 = λH k+1 (where 0 ≤ k ≤ n − 1) belongs to the class of L k -biharmonic, L k -1-type or L k -null-2-type hypersurface. Furthermore, we study the above condition on a well-known family of spacelike hypersurfaces of Lorentz-Minkowski spaces, named the weakly convex hypersurfaces (i.e. on which all of principle curvatures are nonnegative). We prove that, on any weakly convex spacelike hypersurface satisfying the above condition for an integer k (where, 0 ≤ r ≤ n−1), the (k + 1)th mean curvature will be constant. As an interesting result, any weakly convex spacelike hypersurfaces, having assumed to be L k -biharmonic, has to be k-maximal.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.3 20212021-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300711en10.22199/issn.0717-6279-3584
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Spacelike hypersurfaces Lk-biharmonic k-maximal Weakly convex
spellingShingle	Spacelike hypersurfaces Lk-biharmonic k-maximal Weakly convex Pashaie,Firooz Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1
description	Abstract: In this paper, we try to give a classification of spacelike hypersurfaces of the Lorentz-Minkowski space-time E 1 n+1 , whose mean curvature vector field of order (k+ 1) is an eigenvector of the kth linearized operator L k , for a non-negative integer k less than n. The operator L k is defined as the linear part of the first variation of the (k + 1)th mean curvature of a hypersurface arising from its normal variations. We show that any spacelike hypersurface of E 1 n+1 satisfying the condition L k H k+1 = λH k+1 (where 0 ≤ k ≤ n − 1) belongs to the class of L k -biharmonic, L k -1-type or L k -null-2-type hypersurface. Furthermore, we study the above condition on a well-known family of spacelike hypersurfaces of Lorentz-Minkowski spaces, named the weakly convex hypersurfaces (i.e. on which all of principle curvatures are nonnegative). We prove that, on any weakly convex spacelike hypersurface satisfying the above condition for an integer k (where, 0 ≤ r ≤ n−1), the (k + 1)th mean curvature will be constant. As an interesting result, any weakly convex spacelike hypersurfaces, having assumed to be L k -biharmonic, has to be k-maximal.
author	Pashaie,Firooz
author_facet	Pashaie,Firooz
author_sort	Pashaie,Firooz
title	Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1
title_short	Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1
title_full	Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1
title_fullStr	Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1
title_full_unstemmed	Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1
title_sort	weakly convex hypersurfaces of pseudo-euclidean spaces satisfying the condition l k h k+1 = λh k+1
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300711
work_keys_str_mv	AT pashaiefirooz weaklyconvexhypersurfacesofpseudoeuclideanspacessatisfyingtheconditionlkhk1955hk1
_version_	1718439904750338048

Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = &#955;H k+1

Documents similaires

Weakly convex hypersurfaces of pseudo-Euclidean spaces satisfying the condition L k H k+1 = λH k+1