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On the Stability of f-Maximal Spacelike Hypersurfaces in Weighted Generalized Robertson–Walker Spacetimes

Lima E. L. de, Lima H. F. de, Santos F. R. dos

Bulletin of the Polish Academy of Sciences. Mathematics

2016

Vol. 64, no. 2/3

199--208

Our purpose in this paper is to study the stability of f-maximal spacelike hypersurfaces immersed in a weighted generalized Robertson–Walker spacetime −I×ρMnf, where Mnf is a weighted Riemannian manifold endowed with a weight function f. In this setting, we obtain sufficient conditions to guarantee that an f-maximal hypersurface be Lf-stable, where Lf stands for the weighted Jacobi operator.