Geodesic
On the Stability of $f$-Maximal Spacelike Hypersurfaces in Weighted Generalized Robertson–Walker Spacetimes
Eudes L. de Lima 1   ; Henrique F. de Lima 2   ; Fábio R. dos Santos 2
1 Campus Pau dos Ferros Universidade Federal Rural do Semi-Árido 59.900-000 Pau dos Ferros Rio Grande do Norte, Brazil
2 Departamento de Matemática Universidade Federal de Campina Grande 58.429-970 Campina Grande, Paraíba, Brazil
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 64 (2016) no. 2-3, pp. 199-208 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Our purpose in this paper is to study the stability of $f$-maximal spacelike hypersurfaces immersed in a weighted generalized Robertson–Walker spacetime $-I\times _{\rho }M^n_f$, where $M^n_f$ 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 $L_f$-stable, where $L_f$ stands for the weighted Jacobi operator.
DOI : 10.4064/ba8069-8-2016
Keywords: purpose paper study stability f maximal spacelike hypersurfaces immersed weighted generalized robertson walker spacetime i times rho where weighted riemannian manifold endowed weight function setting obtain sufficient conditions guarantee f maximal hypersurface f stable where stands weighted jacobi operator

Eudes L. de Lima  1   ; Henrique F. de Lima  2   ; Fábio R. dos Santos  2

1 Campus Pau dos Ferros Universidade Federal Rural do Semi-Árido 59.900-000 Pau dos Ferros Rio Grande do Norte, Brazil
2 Departamento de Matemática Universidade Federal de Campina Grande 58.429-970 Campina Grande, Paraíba, Brazil 
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     author = {Eudes L. de Lima and Henrique F. de Lima and F\'abio R. dos Santos},
     title = {On the {Stability} of $f${-Maximal} {Spacelike} {Hypersurfaces} in {Weighted} {Generalized} {Robertson{\textendash}Walker} {Spacetimes}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {199--208},
     year = {2016},
     volume = {64},
     number = {2-3},
     doi = {10.4064/ba8069-8-2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba8069-8-2016/}
}
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Eudes L. de Lima; Henrique F. de Lima; Fábio R. dos Santos. On the Stability of $f$-Maximal Spacelike Hypersurfaces in Weighted Generalized Robertson–Walker Spacetimes. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 64 (2016) no. 2-3, pp. 199-208. doi: 10.4064/ba8069-8-2016

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