Any compact spacelike hypersurface immersed in a doubly warped product spacetime I x P with nondecreasing warping factor ρ must be a spacelike slice, provided that the mean curvature satisfies H ≥ ρ′∕hρ 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.

A Note on Spacelike Hypersurfaces and Timelike Conformal Vectors / G. Colombo, J.A.S. Pelegrín, M. Rigoli (RSME SPRINGER SERIES). - In: Recent Advances in Pure and Applied Mathematics / [a cura di] F. Ortegón Gallego, J.I. García García. - [s.l] : Springer, 2020. - ISBN 9783030413200. - pp. 135-147 [10.1007/978-3-030-41321-7_11]

A Note on Spacelike Hypersurfaces and Timelike Conformal Vectors

G. Colombo;M. Rigoli
2020

Abstract

Any compact spacelike hypersurface immersed in a doubly warped product spacetime I x P with nondecreasing warping factor ρ must be a spacelike slice, provided that the mean curvature satisfies H ≥ ρ′∕hρ 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.
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/850628
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