Vol. 292, No. 1, 2018

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ISSN: 0030-8730
New characterizations of linear Weingarten spacelike hypersurfaces in the de Sitter space

Luis J. Alías, Henrique F. de Lima and Fábio R. dos Santos

Vol. 292 (2018), No. 1, 1–19
Abstract

We deal with complete linear Weingarten spacelike hypersurfaces immersed in the de Sitter space, that is, spacelike hypersurfaces of de Sitter space whose mean and scalar curvatures are linearly related. In this setting, we apply a suitable extension of the generalized maximum principle of Omori–Yau to show that either such a spacelike hypersurface must be totally umbilical or there holds a sharp estimate for the norm of its total umbilicity tensor, with equality characterizing hyperbolic cylinders of de Sitter space. We also study the parabolicity of these spacelike hypersurfaces with respect to a Cheng–Yau modified operator.

Keywords
de Sitter space, linear Weingarten hypersurfaces, spacelike hypersurfaces, totally umbilical hypersurfaces, hyperbolic cylinders, parabolicity
Mathematical Subject Classification 2010
Primary: 53C42
Secondary: 53A10, 53C20, 53C50
Milestones
Received: 6 December 2016
Accepted: 1 July 2017
Published: 22 September 2017
Authors
Luis J. Alías
Departamento de Matemáticas
Universidad de Murcia
Campus de Espinardo
Murcia
Spain
Henrique F. de Lima
Departamento de Matemática
Universidade Federal de Campina Grande
Campina Grande, PB
Brazil
Fábio R. dos Santos
Departamento de Matemática
Universidade Federal de Campina Grande
Campina Grande, PB
Brazil