Open AccessOn the umbilicity of linear Weingarten spacelike submanifolds immersed in the de Sitter space
Author(s) -
Weiller F. C. Barboza,
Eudes L. de Lima,
Henrique F. de Lima,
Marco Antonio L. Velásquez
Publication year - 2020
Publication title -
bulletin of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 1664-3607
pISSN - 1664-3615
DOI - 10.1142/s1664360720500228
Subject(s) - submanifold , mean curvature , mathematical physics , second fundamental form , mathematics , curvature , order (exchange) , mathematical analysis , physics , geometry , finance , economics
We investigate the umbilicity of [Formula: see text]-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field in the de Sitter space [Formula: see text] of index [Formula: see text]. We recall that a spacelike submanifold is said to be linear Weingarten when its mean curvature function [Formula: see text] and its normalized scalar curvature [Formula: see text] satisfy a linear relation of the type [Formula: see text], for some constants [Formula: see text]. Under suitable constraints on the values of [Formula: see text] and [Formula: see text], we apply a generalized maximum principle for a modified Cheng–Yau operator [Formula: see text] in order to show that such a spacelike submanifold must be either totally umbilical or isometric to a product [Formula: see text], where the factors [Formula: see text] are totally umbilical submanifolds of [Formula: see text] which are mutually perpendicular along their intersections. Moreover, we also study the case in which these spacelike submanifolds are [Formula: see text]-parabolic.