Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 4, pp. 460-472   https://doi.org/10.15407/mag16.04.460     ( to contents , go back )
https://doi.org/10.15407/mag16.04.460

Remarks on Screen Integrable Null Hypersurfaces in Lorentzian Manifolds

Samuel Ssekajja

School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg-South Africa
E-mail: samuel.ssekajja@wits.ac.za

Received September 23, 2019, revised February 20, 2020.

Abstract

In the present paper, we show that the geometry of a screen integrablenull hypersurface can be generated from an isometric immersion of a leafof its screen distribution into the ambient space. We prove, under certaingeometric 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, the examplesare given to illustrate the main ideas.

Mathematics Subject Classification 2010: 53C25, 53C40, 53C50
Key words: screen integrable null hypersurfaces, normal curvature tensorof a leaf

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