Geodesic
On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 4, pp. 515-529.

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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.
DOI : 10.14712/1213-7243.2015.137
Classification : 53A10, 53C20, 53C42, 53C50
Keywords: locally symmetric Riemannian manifolds; Einstein manifolds; complete linear Weingarten hypersurfaces; totally umbilical hypersurfaces; isoparametric hypersurfaces 
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     title = {On complete linear {Weingarten} hypersurfaces in locally symmetric {Riemannian} manifolds},
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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. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 4, pp. 515-529. doi : 10.14712/1213-7243.2015.137. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.137/

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