Abstract: In this paper, we deal with n-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space L_{p}^{n+p} of index p>1, which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric submanifold of the ambient space. For this, we use three main core analytical tools: a suitable version of the Omori-Yau maximum principle, parabolicity with respect to a modified Cheng-Yau operator and a certain integrability property.
Keywords: locally symmetric semi-Riemannian space; mean curvature vector field; complete linear Weingarten spacelike submanifold; totally umbilical submanifold; isoparametric submanifold; \mathcal L-parabolicity
DOI: DOI 10.14712/1213-7243.2023.013
AMS Subject Classification: 53C42 53C21 53C50