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Rigidity results for complete spacelike submanifolds in plane fronted waves

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.

preprint2022arXivOpen access
Francisco J. PalomoJosé A. S. PelegrínAlfonso Romero
math.DG
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Francisco J. PalomoJosé A. S. PelegrínAlfonso Romero

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