Rigidity results for complete spacelike submanifolds in plane fronted waves

Palomo, Francisco J.; Romero Sarabia, Alfonso

doi:10.1007/s13398-022-01315-4

s13398-022-01315-4.pdf (279.7Kb)

Identificadores

URI: https://hdl.handle.net/10481/77122

DOI: 10.1007/s13398-022-01315-4

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Editorial

Springer

Materia

Extremal submanifold

Weakly trapped submanifold

Plane fronted wave

Fecha

2022-09-08

Referencia bibliográfica

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]

Patrocinador

Spanish Government PID2020-118452GBI00 PID2020-116126GB-I00; ERDF project P20-01391; "Maria de Maeztu" Excellence Unit IMAG - MCIN-AEI CEX2020-001105-M

Resumen

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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