Hostname: page-component-6bf8c574d5-t27h7 Total loading time: 0 Render date: 2025-02-27T04:31:16.770Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong (r, s)-stability in the de Sitter space

Published online by Cambridge University Press:  30 January 2015

Henrique F. de Lima ,
Antonio F. de Sousa  and
Marco Antonio L. Velásquez
Henrique F. de Lima
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58109-970 Campina Grande, Paraíba, Brazil, ([email protected])
Antonio F. de Sousa
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco, 50740-560 Recife, Pernambuco, Brazil
Marco Antonio L. Velásquez
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58109-970 Campina Grande, Paraíba, Brazil
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we establish the notion of strong (r, s)-stability concerning closed space-like hypersurfaces immersed with higher-order mean curvatures linearly related in the de Sitter space . In this setting, we prove that totally umbilical round spheres of are strongly (r, s)-stable. Afterwards, we obtain sufficient geometric conditions that guarantee that a closed strongly (r, s)-stable space-like hypersurface in must be a totally umbilical round sphere.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 1 , February 2015 , pp. 91 - 104
Copyright
Copyright © Royal Society of Edinburgh 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)