On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds

Cícero P. Aquino; Henrique F. de Lima; Fábio R. dos Santos; Marco Antonio L. Velásquez

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 4, page 515-529
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Aquino, Cícero P., et al. "On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds." Commentationes Mathematicae Universitatis Carolinae 56.4 (2015): 515-529. <http://eudml.org/doc/276197>.

@article{Aquino2015,
abstract = {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.},
author = {Aquino, Cícero P., de Lima, Henrique F., dos Santos, Fábio R., Velásquez, Marco Antonio L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally symmetric Riemannian manifolds; Einstein manifolds; complete linear Weingarten hypersurfaces; totally umbilical hypersurfaces; isoparametric hypersurfaces},
language = {eng},
number = {4},
pages = {515-529},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds},
url = {http://eudml.org/doc/276197},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Aquino, Cícero P.
AU - de Lima, Henrique F.
AU - dos Santos, Fábio R.
AU - Velásquez, Marco Antonio L.
TI - On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 4
SP - 515
EP - 529
AB - 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.
LA - eng
KW - locally symmetric Riemannian manifolds; Einstein manifolds; complete linear Weingarten hypersurfaces; totally umbilical hypersurfaces; isoparametric hypersurfaces
UR - http://eudml.org/doc/276197
ER -

References

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