Rigidity results for complete spacelike submanifolds in plane fronted waves
Differential Geometry
2022-02-01 v1
Abstract
New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a complete spacelike submanifold in these spacetimes is contained in a characteristic lightlike hypersurface. Moreover, for a complete codimension two extremal submanifold in a plane fronted wave we show sufficient conditions to guarantee that it is a (totally geodesic) wavefront.
Keywords
Cite
@article{arxiv.2201.13350,
title = {Rigidity results for complete spacelike submanifolds in plane fronted waves},
author = {Francisco J. Palomo and José A. S. Pelegrín and Alfonso Romero},
journal= {arXiv preprint arXiv:2201.13350},
year = {2022}
}