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Article

Aquino, Cícero P. ; de Lima, Henrique F. ; dos Santos, Fábio R. ; Velásquez, Marco Antonio L.
On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 56 (2015), issue 4, pp. 515-529
MSC: 53A10, 53C20, 53C42, 53C50 | MR 3434226 | Zbl 06537721 | DOI: 10.14712/1213-7243.2015.137
Keywords:
locally symmetric Riemannian manifolds; Einstein manifolds; complete linear Weingarten hypersurfaces; totally umbilical hypersurfaces; isoparametric hypersurfaces
Summary:
Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.
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