Rigidity results for complete spacelike submanifolds in plane fronted waves
Autor
Palomo, Francisco J.
Pelegrín, José A. S.
Romero, Alfonso
Editor
SpringerFecha
2022Materia
Extremal submanifoldWeakly trapped submanifold
Plane fronted wave
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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.