-parabolic linear Weingarten spacelike submanifolds immersed in an Einstein manifold
Railane Antonia
Universidade Federal da Paraíba, João Pessoa, BrazilHenrique Fernandes de Lima
Universidade Federal de Campina Grande, Brazil
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Abstract
In this paper, we deal with complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector and flat normal bundle in an Einstein manifold of index . Under some curvature constraints on the ambient space, we establish an -parabolicity criterion related to a suitable modified Cheng–Yau's operator and we apply it to obtain sufficient conditions which guarantee that such a spacelike submanifold must be an isoparametric hypersurface of with two distinct principal curvatures one of which is simple.
Cite this article
Railane Antonia, Henrique Fernandes de Lima, -parabolic linear Weingarten spacelike submanifolds immersed in an Einstein manifold. Port. Math. 79 (2022), no. 3/4, pp. 211–224
DOI 10.4171/PM/2082