On the Stability of $f$-Maximal Spacelike Hypersurfaces in Weighted Generalized Robertson–Walker Spacetimes
Volume 64 / 2016
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.
