2022/11/15 by Alberto Soria, Soria, Alberto
Mathematics · Physics and Astronomy · #53C42 #53C50 #53C80 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2211.08495
openalex publication_date 2022/11/15 · openalex created_date 2022/11/25 · openalex updated_date 2026/07/28
In this article spacelike hypersurfaces immersed in twisted product spacetimes I×f F with complete fiber are studied. Several conditions ensuring global hyperbolicity are presented, as well as a relation that needs to hold on each spacelike hypersurface in I×f F for it to be a simple warped product. When the fiber is assumed to be closed (compact and without boundary) and the ambient spacetime has a suitable expanding behaviour, non-existence results for constant mean curvature hypersurfaces are obtained. Under the same hypothesis, a characterization of compact maximal hypersurfaces and other for totally umbilic ones with a suitable restriction on their mean curvature are presented. The description of maximal hypersurfaces in twisted product spacetimes of the form I f × F with a one-dimensional Lorentzian fiber is also included. Finally, the mean curvature equation for a spacelike graph on the fiber is computed and as an application, some Calabi-Bernstein-type results are proven. We also include in an Appendix some known conformal geometry results describing the transformation of relevant tensors and operators under the action of a conformal map in a pseudo-Riemannian background.