Rigidity results for complete spacelike submanifolds in plane fronted waves

2022/01/31 by Francisco J. Palomo, Palomo, Francisco J., José A. S. Pelegrín +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG

paper · pdf · doi:10.48550/arxiv.2201.13350

arxiv created 2022/01/31 · openalex publication_date 2022/01/31 · arxiv updated 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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