Abstract
In this paper, we establish new characterizations of totally geodesic spacelike hypersurfaces immersed in a generalized Robertson–Walker spacetime, which is supposed to obey the null convergence condition. As applications, we get nonparametric results concerning to entire maximal vertical graphs in a such ambient spacetime. Proceeding, we obtain a lower estimate of the index of relative nullity of complete r-maximal spacelike hypersurfaces immersed in Robertson–Walker spacetimes of constant sectional curvature. In particular, we prove a sort of weak extension of the classical Calabi–Bernstein theorem.
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de Lima, H.F., Parente, U.L. On the geometry of maximal spacelike hypersurfaces immersed in a generalized Robertson–Walker spacetime. Annali di Matematica 192, 649–663 (2013). https://doi.org/10.1007/s10231-011-0241-y
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DOI: https://doi.org/10.1007/s10231-011-0241-y
Keywords
- Generalized Robertson–Walker spacetimes
- Complete r-maximal spacelike hypersurfaces
- Totally geodesic spacelike hypersurfaces
- Null convergence condition
- Entire vertical graphs
- Index of relative nullity