2016/02/12 by José A. S. Pelegrín, Alfonso Romero, Rafael M. Rubio
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #Constant (computer programming) #Constant curvature #Curvature #Extension (predicate logic) #Geodesic #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hypersurface #Lorentz transformation #Mathematical analysis #Mathematical physics #Mathematics #Mean curvature #Physics #Pure mathematics #Totally geodesic #Vector field #math.DG #msc:53C42 #msc:53C50 #msc:53C80
paper · pdf · doi:10.1088/0264-9381/33/5/055003
published as Classical and Quantum Gravity, Volume 33 (2016), Number 5, 055003
openalex publication_date 2016/02/12 · arxiv created 2016/04/28 · arxiv updated 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study constant mean curvature spacelike hypersurfaces and in particular maximal hypersurfaces immersed in pp-wave spacetimes satisfying the timelike convergence condition. We prove the non-existence of compact spacelike hypersurfaces whose constant mean curvature is non-zero and also that every compact maximal hypersurface is totally geodesic. Moreover, we give an extension of the classical Calabi–Bernstein theorem to this class of pp-wave spacetimes.