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

Volume 64 / 2016

Eudes L. de Lima, Henrique F. de Lima, Fábio R. dos Santos Bulletin Polish Acad. Sci. Math. 64 (2016), 199-208 MSC: Primary 53C42; Secondary 53B30, 53C50. DOI: 10.4064/ba8069-8-2016 Published online: 30 September 2016

Abstract

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.

Authors

  • Eudes L. de LimaCampus Pau dos Ferros
    Universidade Federal Rural do Semi-Árido
    59.900-000 Pau dos Ferros
    Rio Grande do Norte, Brazil
    e-mail
  • Henrique F. de LimaDepartamento de Matemática
    Universidade Federal de Campina Grande
    58.429-970 Campina Grande, Paraíba, Brazil
    e-mail
  • Fábio R. dos SantosDepartamento de Matemática
    Universidade Federal de Campina Grande
    58.429-970 Campina Grande, Paraíba, Brazil
    e-mail

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