Remarks on screen integrable null hypersurfaces in Lorentzian manifolds

2019/06/12 by Ssekajja, Samuel
#53C25 #53C40 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.05281

Abstract

In the present paper, we show that the geometry of a screen integrable null hypersurface can be generated from an isometric immersion of a leaf of its screen distribution into the ambient space. We prove, under certain geometric conditions, that such immersions are contained in semi-Euclidean spheres or hyperbolic spaces, and the underlying null hypersurfaces are necessarily umbilic and screen totally umbilic. Where necessary, examples have been given to illustrate the main ideas.

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