RT Journal Article
T1 A Curvature Inequality Characterizing Totally Geodesic Null Hypersurfaces
A1 Olea-Andrades, Benjamín
K1 Hipersuperficies
K1 Geometría diferencial
AB A well-known application of the Raychaudhuri equation showsthat, under geodesic completeness, totally geodesic null hypersurfacesare unique which satisfy that the Ricci curvature is nonnegative in thenull direction. The proof of this fact is based on a direct analysis ofa differential inequality. In this paper, we show, without assuming thegeodesic completeness, that an inequality involving the squared nullmean curvature and the Ricci curvature in a compact three-dimensionalnull hypersurface also implies that it is totally geodesic. The proof iscompletely different from the above, since Riemannanian tools are usedin the null hypersurface thanks to the rigging technique.
PB Springer
YR 2023
FD 2023
LK https://hdl.handle.net/10630/26277
UL https://hdl.handle.net/10630/26277
LA eng
NO 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
NO Funding for open access publishing: Universidad Málaga/CBUA.Funding for open access charge: Universidad de Málaga / CBUA.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026