| Full text | |
| Author(s): |
Lobos, Guillermo A.
;
Melara, Mynor
;
Santos, Maria R. B.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Results in Mathematics; v. 79, n. 8, p. 22-pg., 2024-12-01. |
| Abstract | |
We determine a Simons type formula for spacelike submanifolds within a broad class of semi-Riemannian warped products, which includes the Robertson-Walker spacetimes. This formula enables us to extend results well-known from Riemannian geometry to the semi-Riemannian case. Specifically, when the ambient space has constant sectional curvature, such as Lorentz-Minkowski, de Sitter and anti-de Sitter spacetimes, we establish that compact spacelike hypersurfaces with parallel mean curvature vector field and non-negative sectional curvature are isoparametric hypersurfaces. This result constitutes a generalization of the Riemannian case within space forms, as demonstrated by Nomizu and Smyth in 1969. As an application, we extend analogous results previously established for pseudo-parallel immersions in Riemannian space forms. With this extension, we prove that any semi-parallel spacelike hypersurface with zero mean curvature into de Sitter spacetime is totally geodesic. Furthermore, we show that there are no semi-parallel spacelike hypersurfaces with zero mean curvature into Einstein-de Sitter spacetime. (AU) | |
| FAPESP's process: | 22/16097-2 - Modern methods in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |