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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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