On maximal hypersurfaces in Lorentz manifolds admitting a parallel lightlike vector field
Differential Geometry
2016-04-29 v1
Abstract
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.
Cite
@article{arxiv.1604.08545,
title = {On maximal hypersurfaces in Lorentz manifolds admitting a parallel lightlike vector field},
author = {José A. S. Pelegrín and Alfonso Romero and Rafael M. Rubio},
journal= {arXiv preprint arXiv:1604.08545},
year = {2016}
}