Rigidity results for complete spacelike submanifolds in plane fronted waves

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s13398-022-01315-4.pdf (279.8 KB)

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URI: https://hdl.handle.net/10630/24959
DOI: https://doi.org/10.1007/s13398-022-01315-4

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2022-09-08

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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.

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Palomo, F.J., Pelegrín, J.A.S. & Romero, A. Rigidity results for complete spacelike submanifolds in plane fronted waves. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 179 (2022). https://doi.org/10.1007/s13398-022-01315-4

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Atribución 4.0 Internacional
Except where otherwised noted, this item's license is described as Atribución 4.0 Internacional