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oai:riuma.uma.es:10630/262772026-02-03T11:30:08Zcom_10630_2254col_10630_37953

A Curvature Inequality Characterizing Totally Geodesic Null Hypersurfaces Olea-Andrades, Benjamín Hipersuperficies Geometría diferencial A well-known application of the Raychaudhuri equation shows that, under geodesic completeness, totally geodesic null hypersurfaces are unique which satisfy that the Ricci curvature is nonnegative in the null direction. The proof of this fact is based on a direct analysis of a differential inequality. In this paper, we show, without assuming the geodesic completeness, that an inequality involving the squared null mean curvature and the Ricci curvature in a compact three-dimensional null hypersurface also implies that it is totally geodesic. The proof is completely different from the above, since Riemannanian tools are used in the null hypersurface thanks to the rigging technique. 2023-04-18T11:27:34Z 2023-04-18T11:27:34Z 2023 journal article Olea. (2023). A Curvature Inequality Characterizing Totally Geodesic Null Hypersurfaces. Mediterranean Journal of Mathematics, 20(2). https://doi.org/10.1007/s00009-023-02285-6 https://hdl.handle.net/10630/26277 https://doi.org/10.1007/s00009-023-02285-6 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer