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arXiv · 2109.04164

A note on spacelike hypersurfaces and timelike conformal vectors

Giulio Colombo·José A. S. Pelegrín·Marco Rigoli
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Abstract

Any compact spacelike hypersurface immersed in a doubly warped product spacetime $I{}_{h} \times_{\rho} \mathbb{P}$ with nondecreasing warping factor $\rho$ must be a spacelike slice, provided that the mean curvature satisfies $H\geq\rho'/h\rho$ everywhere on the hypersurface. The conclusion also holds, under suitable assumptions on the immersion, when the hypersurface is complete and noncompact. A similar rigidity property is shown for compact hypersurfaces in spacetimes carrying a conformal, strictly expanding, timelike vector field.

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Giulio Colombo, José A. S. Pelegrín, Marco Rigoli. 2021-09-09. A note on spacelike hypersurfaces and timelike conformal vectors. https://doi.org/10.1007/978-3-030-41321-7

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