CHARACTERIZATIONS OF LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN EINSTEIN SPACETIMES
2013 ◽
Vol 55
(3)
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pp. 567-579
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Keyword(s):
AbstractOur 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.
2012 ◽
Vol 20
(1)
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pp. 387-406
Keyword(s):
2011 ◽
Vol 151
(2)
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pp. 271-282
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1979 ◽
Vol 82
(3-4)
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pp. 233-240
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2011 ◽
Vol 29
(3)
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pp. 279-291