Geodesic
CHARACTERIZATIONS OF LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN EINSTEIN SPACETIMES
Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 567-579

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DOI

Our purpose is to study the geometry of linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Einstein spacetime, whose sectional curvature is supposed to obey some standard restrictions. In this setting, by using as main analytical tool a generalized maximum principle for complete non-compact Riemannian manifolds, 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. Applications to the de Sitter space are given.
DOI : 10.1017/S0017089512000754
Mots-clés : Primary 53C42, Secondary 53A10, 53B30 and 53C50 
LIMA, HENRIQUE F. DE; LIMA, JOSEÍLSON R. DE. CHARACTERIZATIONS OF LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN EINSTEIN SPACETIMES. Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 567-579. doi: 10.1017/S0017089512000754
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     author = {LIMA, HENRIQUE F. DE and LIMA, JOSE\'ILSON R. DE},
     title = {CHARACTERIZATIONS {OF} {LINEAR} {WEINGARTEN} {SPACELIKE} {HYPERSURFACES} {IN} {EINSTEIN} {SPACETIMES}},
     journal = {Glasgow mathematical journal},
     pages = {567--579},
     year = {2013},
     volume = {55},
     number = {3},
     doi = {10.1017/S0017089512000754},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000754/}
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